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    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
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    <link:label id="lab_dei_Security12bTitle_019f9eb7-cb83-7fec-a93f-cd733697ccce_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventMember_019fed01-190a-77de-bb4f-2c72d3d046a7_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019fa5eb-68d6-7a8d-bfb0-e5b67fada3ad_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss attributed to common stockholders - diluted</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019fd281-5421-7ba2-914a-99a691bb7d18_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Adjusted net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
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    <link:label id="lab_dei_DocumentFiscalYearFocus_019f9eb7-cb83-7f69-8610-a899d77f8f89_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueOptionPricingModelMember_019fafc9-b499-78f0-99f5-3aad137094c3_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Technique, Option Pricing Model</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueOptionPricingModelMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Option Pricing Model [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueOptionPricingModelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:to="lab_us-gaap_ValuationTechniqueOptionPricingModelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019fa5a6-3a6f-76ec-bdc0-f6f81945786a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_019f9ed9-873e-730a-b939-ebdf27fe519c_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation and benefits</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_MeasurementInputQualifiedFinancingScenarioMember_019fafe3-d48e-7b01-9068-128c39cb3563_terseLabel_en-US" xlink:label="lab_fac_MeasurementInputQualifiedFinancingScenarioMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Qualified Financing Scenario</link:label>
    <link:label id="lab_fac_MeasurementInputQualifiedFinancingScenarioMember_label_en-US" xlink:label="lab_fac_MeasurementInputQualifiedFinancingScenarioMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Qualified Financing Scenario [Member]</link:label>
    <link:label id="lab_fac_MeasurementInputQualifiedFinancingScenarioMember_documentation_en-US" xlink:label="lab_fac_MeasurementInputQualifiedFinancingScenarioMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Qualified Financing Scenario</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_MeasurementInputQualifiedFinancingScenarioMember" xlink:href="fac-20260630.xsd#fac_MeasurementInputQualifiedFinancingScenarioMember"/>
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    <link:label id="lab_dei_EntityExTransitionPeriod_019f9eb7-cb83-73f2-881d-9354a73fdaf2_terseLabel_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:label id="lab_dei_EntityExTransitionPeriod_label_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityExTransitionPeriod"/>
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    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_019fafa8-e21e-76da-930b-2aca9aafdd04_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:to="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_019fb571-a150-702a-9571-14e48eaf72d5_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of securities called by warrants or rights (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:to="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1_019fca19-9a18-70c1-b49b-fd8f3950c755_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion price (in usd per share)</link:label>
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    <link:label id="lab_fac_AdjustmentsToAdditionalPaidInCapitalReclassificationOfWarrantLiabilityFromEquity_019fd880-513f-77b7-820e-51af51ae3052_negatedTerseLabel_en-US" xlink:label="lab_fac_AdjustmentsToAdditionalPaidInCapitalReclassificationOfWarrantLiabilityFromEquity" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reclassification of warrant liability&#160;for Series A Common Stock&#160;from equity</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_fac_AdjustmentsToAdditionalPaidInCapitalReclassificationOfWarrantLiabilityFromEquity" xlink:href="fac-20260630.xsd#fac_AdjustmentsToAdditionalPaidInCapitalReclassificationOfWarrantLiabilityFromEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_AdjustmentsToAdditionalPaidInCapitalReclassificationOfWarrantLiabilityFromEquity" xlink:to="lab_fac_AdjustmentsToAdditionalPaidInCapitalReclassificationOfWarrantLiabilityFromEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019f9eb7-cb83-725a-b18f-2b2f64d6986b_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_019fa5a6-3a6f-73af-b996-47d6a552e816_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019f9eb7-cb83-76e5-ae48-9b9a50d04991_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_019fa621-f29d-7b41-97a4-d95e1ef11250_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Principal paid on finance lease liability</link:label>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_label_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:to="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightTable_019fcf9d-3f62-7335-ae9b-cab125e0ff91_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Table]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightTable_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightTable" xlink:to="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_019fab6e-9911-74c2-acbe-4c2373c6001b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of convertible promissory notes</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Issuances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAdjustmentOfWarrants_019fd280-49cc-73b2-8d37-3e14cc8007c9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueAdjustmentOfWarrants" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of warrant liabilities for Series B-1 and Series D redeemable convertible preferred stock</link:label>
    <link:label id="lab_us-gaap_FairValueAdjustmentOfWarrants_019fa614-96d9-7fb4-b8a6-1f536863f8b7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAdjustmentOfWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of warrant liabilities for Series B-1 and Series D redeemable convertible preferred stock</link:label>
    <link:label id="lab_us-gaap_FairValueAdjustmentOfWarrants_019fcfc8-571b-7210-9a56-e7f638bdcee9_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueAdjustmentOfWarrants" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of Private warrant liability</link:label>
    <link:label id="lab_us-gaap_FairValueAdjustmentOfWarrants_label_en-US" xlink:label="lab_us-gaap_FairValueAdjustmentOfWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment of Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAdjustmentOfWarrants" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAdjustmentOfWarrants"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAdjustmentOfWarrants" xlink:to="lab_us-gaap_FairValueAdjustmentOfWarrants" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_019fcfce-5df9-77ed-9d56-fe4d82449e98_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_JasonDuvaMember_label_en-US" xlink:label="lab_fac_JasonDuvaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jason Duva [Member]</link:label>
    <link:label id="lab_fac_JasonDuvaMember_documentation_en-US" xlink:label="lab_fac_JasonDuvaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jason Duva</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_JasonDuvaMember" xlink:href="fac-20260630.xsd#fac_JasonDuvaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_JasonDuvaMember" xlink:to="lab_fac_JasonDuvaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019fca9d-0222-7a48-bd8c-bd0e56f839ba_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RELATED PARTY TRANSACTIONS</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ValuationApproachAndTechniqueConcentrationPercent_019fdc93-6a15-7f05-9af1-893497a04e14_terseLabel_en-US" xlink:label="lab_fac_ValuationApproachAndTechniqueConcentrationPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation approach and technique concentration (in percent)</link:label>
    <link:label id="lab_fac_ValuationApproachAndTechniqueConcentrationPercent_label_en-US" xlink:label="lab_fac_ValuationApproachAndTechniqueConcentrationPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach And Technique, Concentration, Percent</link:label>
    <link:label id="lab_fac_ValuationApproachAndTechniqueConcentrationPercent_documentation_en-US" xlink:label="lab_fac_ValuationApproachAndTechniqueConcentrationPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Approach And Technique, Concentration, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ValuationApproachAndTechniqueConcentrationPercent" xlink:href="fac-20260630.xsd#fac_ValuationApproachAndTechniqueConcentrationPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ValuationApproachAndTechniqueConcentrationPercent" xlink:to="lab_fac_ValuationApproachAndTechniqueConcentrationPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019f9eb7-cb82-7251-b485-f182ebb36a1f_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_019fb51f-2c0d-739d-990c-6742d75dfcc3_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Grants in period (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_019fce4a-a949-7b63-a75f-b5e33391f60e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustments</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_BuildingFixturesMember_019f9ec2-034e-710a-9ee2-98a2181186bf_terseLabel_en-US" xlink:label="lab_fac_BuildingFixturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building Fixtures</link:label>
    <link:label id="lab_fac_BuildingFixturesMember_label_en-US" xlink:label="lab_fac_BuildingFixturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building Fixtures [Member]</link:label>
    <link:label id="lab_fac_BuildingFixturesMember_documentation_en-US" xlink:label="lab_fac_BuildingFixturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Building Fixtures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_BuildingFixturesMember" xlink:href="fac-20260630.xsd#fac_BuildingFixturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_BuildingFixturesMember" xlink:to="lab_fac_BuildingFixturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019fa5a6-3a6f-7829-8ca1-ea017cb226ec_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in usd per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019fab5b-344d-7c26-bf64-53354338eb15_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ValuationApproachTechniqueScenarioBasedMethodMember_019fafda-b661-7a3c-bd31-bac144d007ed_terseLabel_en-US" xlink:label="lab_fac_ValuationApproachTechniqueScenarioBasedMethodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach Technique, Scenario Based Method</link:label>
    <link:label id="lab_fac_ValuationApproachTechniqueScenarioBasedMethodMember_label_en-US" xlink:label="lab_fac_ValuationApproachTechniqueScenarioBasedMethodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach Technique, Scenario Based Method [Member]</link:label>
    <link:label id="lab_fac_ValuationApproachTechniqueScenarioBasedMethodMember_documentation_en-US" xlink:label="lab_fac_ValuationApproachTechniqueScenarioBasedMethodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Approach Technique, Scenario Based Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ValuationApproachTechniqueScenarioBasedMethodMember" xlink:href="fac-20260630.xsd#fac_ValuationApproachTechniqueScenarioBasedMethodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ValuationApproachTechniqueScenarioBasedMethodMember" xlink:to="lab_fac_ValuationApproachTechniqueScenarioBasedMethodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019fcfca-ba25-769e-8f6d-198044de639e_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average common stock outstanding - basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019fa5eb-68d6-79a5-ad06-35615ca74c07_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_DerivativeLiabilityMember_019fafb5-ab51-7a9b-a3c0-477e828be819_terseLabel_en-US" xlink:label="lab_fac_DerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant Liabilities</link:label>
    <link:label id="lab_fac_DerivativeLiabilityMember_label_en-US" xlink:label="lab_fac_DerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Member]</link:label>
    <link:label id="lab_fac_DerivativeLiabilityMember_documentation_en-US" xlink:label="lab_fac_DerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_DerivativeLiabilityMember" xlink:href="fac-20260630.xsd#fac_DerivativeLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_DerivativeLiabilityMember" xlink:to="lab_fac_DerivativeLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_AccruedTransactionCostsCurrent_019f9ed9-873e-7e66-9b19-018111abb2ad_terseLabel_en-US" xlink:label="lab_fac_AccruedTransactionCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued transaction costs</link:label>
    <link:label id="lab_fac_AccruedTransactionCostsCurrent_label_en-US" xlink:label="lab_fac_AccruedTransactionCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Transaction Costs, Current</link:label>
    <link:label id="lab_fac_AccruedTransactionCostsCurrent_documentation_en-US" xlink:label="lab_fac_AccruedTransactionCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Transaction Costs, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_AccruedTransactionCostsCurrent" xlink:href="fac-20260630.xsd#fac_AccruedTransactionCostsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_AccruedTransactionCostsCurrent" xlink:to="lab_fac_AccruedTransactionCostsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember_019faf8f-98c9-734a-96b8-90618a808500_terseLabel_en-US" xlink:label="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
    <link:label id="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember_label_en-US" xlink:label="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019fca89-7b1e-7594-87f2-1e9be52d2f28_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_019fa5a6-3a6f-7565-85fe-d7c39866412e_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesB1RedeemableConvertiblePreferredStockMember_019fa5c7-f793-7e4b-8d91-ae52bdf3944e_terseLabel_en-US" xlink:label="lab_fac_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series B-1 redeemable convertible preferred stock</link:label>
    <link:label id="lab_fac_SeriesB1RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_fac_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series B-1 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_fac_SeriesB1RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_fac_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series B-1 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:href="fac-20260630.xsd#fac_SeriesB1RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:to="lab_fac_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertibleDebtNoncurrent_019fa5b9-f567-7f3c-b05b-5a1435501e1b_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertibleDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible promissory notes &#8211; related parties, at fair value</link:label>
    <link:label id="lab_us-gaap_ConvertibleDebtNoncurrent_label_en-US" xlink:label="lab_us-gaap_ConvertibleDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Debt, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertibleDebtNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertibleDebtNoncurrent" xlink:to="lab_us-gaap_ConvertibleDebtNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ConversionOfWarrantLiabilitiesForCommonStock_019fa64b-a931-7443-b5e6-897250ad701c_terseLabel_en-US" xlink:label="lab_fac_ConversionOfWarrantLiabilitiesForCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of warrant liabilities for Series B-1 and Series D into Series A Common Stock</link:label>
    <link:label id="lab_fac_ConversionOfWarrantLiabilitiesForCommonStock_label_en-US" xlink:label="lab_fac_ConversionOfWarrantLiabilitiesForCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion Of Warrant Liabilities For Common Stock</link:label>
    <link:label id="lab_fac_ConversionOfWarrantLiabilitiesForCommonStock_documentation_en-US" xlink:label="lab_fac_ConversionOfWarrantLiabilitiesForCommonStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Conversion Of Warrant Liabilities For Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ConversionOfWarrantLiabilitiesForCommonStock" xlink:href="fac-20260630.xsd#fac_ConversionOfWarrantLiabilitiesForCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ConversionOfWarrantLiabilitiesForCommonStock" xlink:to="lab_fac_ConversionOfWarrantLiabilitiesForCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019f9eb7-cb82-7da2-be27-8fb62d5cf2d2_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_MeasurementInputRemainingContractualTermMember_019fd7b5-5c5e-7a4f-9f07-58ebe84ad257_terseLabel_en-US" xlink:label="lab_fac_MeasurementInputRemainingContractualTermMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining contractual term</link:label>
    <link:label id="lab_fac_MeasurementInputRemainingContractualTermMember_label_en-US" xlink:label="lab_fac_MeasurementInputRemainingContractualTermMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Remaining Contractual Term [Member]</link:label>
    <link:label id="lab_fac_MeasurementInputRemainingContractualTermMember_documentation_en-US" xlink:label="lab_fac_MeasurementInputRemainingContractualTermMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Remaining Contractual Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_MeasurementInputRemainingContractualTermMember" xlink:href="fac-20260630.xsd#fac_MeasurementInputRemainingContractualTermMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_MeasurementInputRemainingContractualTermMember" xlink:to="lab_fac_MeasurementInputRemainingContractualTermMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019fab7c-3775-732b-aded-27985f416bf6_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_019fb53e-0d3c-7084-9b2f-c5ad022e7b8b_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019fd2ac-c399-74c8-bea5-5fe4894a94cf_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019fa5c6-0d49-7b3d-9e9d-bf1484a36904_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019fd79c-6d92-75c3-9d03-0d2538ca213c_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to common stockholders - basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_MeasurementInputDissolutionScenarioMember_019fafe4-a69a-7f64-8754-9617ccfbf9a8_terseLabel_en-US" xlink:label="lab_fac_MeasurementInputDissolutionScenarioMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dissolution Scenario</link:label>
    <link:label id="lab_fac_MeasurementInputDissolutionScenarioMember_label_en-US" xlink:label="lab_fac_MeasurementInputDissolutionScenarioMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Dissolution Scenario [Member]</link:label>
    <link:label id="lab_fac_MeasurementInputDissolutionScenarioMember_documentation_en-US" xlink:label="lab_fac_MeasurementInputDissolutionScenarioMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Dissolution Scenario</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_MeasurementInputDissolutionScenarioMember" xlink:href="fac-20260630.xsd#fac_MeasurementInputDissolutionScenarioMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_MeasurementInputDissolutionScenarioMember" xlink:to="lab_fac_MeasurementInputDissolutionScenarioMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019fab59-ec1f-7be3-aa24-7b9b73623d76_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_019fcfc7-380e-7fe3-b825-aef298cef50a_terseLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expense), net:</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays_019fcfab-3940-73af-90a0-dcce7373bae5_terseLabel_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption, threshold volume weighted average price trading days</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays_label_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Redemption, Threshold Volume Weighted Average Price Trading Days</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays_documentation_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Redemption, Threshold Volume Weighted Average Price Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays" xlink:href="fac-20260630.xsd#fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays" xlink:to="lab_fac_ClassOfWarrantOrRightRedemptionThresholdVolumeWeightedAveragePriceTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable_019faf8f-98c9-74fa-9c67-1435dd25b7bb_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable" xlink:to="lab_us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_DirectorMembersMember_019fd890-a7bd-7464-87c9-a477f081c046_terseLabel_en-US" xlink:label="lab_fac_DirectorMembersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Director Members</link:label>
    <link:label id="lab_fac_DirectorMembersMember_label_en-US" xlink:label="lab_fac_DirectorMembersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Director Members [Member]</link:label>
    <link:label id="lab_fac_DirectorMembersMember_documentation_en-US" xlink:label="lab_fac_DirectorMembersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Director Members</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_DirectorMembersMember" xlink:href="fac-20260630.xsd#fac_DirectorMembersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_DirectorMembersMember" xlink:to="lab_fac_DirectorMembersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_019fed01-190a-776d-bc65-82689f572e00_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019fb57c-8709-7149-ac45-7415e2c2a103_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionPricePerShare_019fcfa1-30c0-72dd-9fb2-a67ff235e77c_terseLabel_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption, price per share (in usd per share)</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionPricePerShare_label_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption, Price Per Share</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionPricePerShare_documentation_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ClassOfWarrantOrRightRedemptionPricePerShare" xlink:href="fac-20260630.xsd#fac_ClassOfWarrantOrRightRedemptionPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ClassOfWarrantOrRightRedemptionPricePerShare" xlink:to="lab_fac_ClassOfWarrantOrRightRedemptionPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019faf1d-0a12-7b6e-89b7-a8e974c4b82d_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandMember_019f9ec2-034e-7705-ba0a-a1e246ad93f3_terseLabel_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_LandMember_label_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandMember" xlink:to="lab_us-gaap_LandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019fdc9b-e63b-7e8e-b088-b67e5a85b2ec_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_019fa615-c6ba-756c-b9d7-d743bdcff281_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss (gain) on disposal of property and equipment</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Disposition of Property Plant Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:to="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_019faf19-7dc3-7543-97e1-a6efafcd7097_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
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    <link:label id="lab_fac_ReclassificationOfWarrantLiabilityFromEquity_label_en-US" xlink:label="lab_fac_ReclassificationOfWarrantLiabilityFromEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification Of Warrant Liability From Equity</link:label>
    <link:label id="lab_fac_ReclassificationOfWarrantLiabilityFromEquity_documentation_en-US" xlink:label="lab_fac_ReclassificationOfWarrantLiabilityFromEquity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reclassification Of Warrant Liability From Equity</link:label>
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    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019fcfd5-c28f-7026-abec-e8399c7c21da_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Financing costs related to issuance of convertible promissory notes</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019fab6e-9911-7a71-9382-2b8e9f617248_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
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    <link:label id="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_019f9ed1-5e66-717b-b6cb-e15fa24e9baa_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accrued Expenses</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accrued Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019fab63-761f-7976-a441-2bedaf41633b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_019fcf9d-3f62-7349-be2d-e242c5b1bfd3_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise price (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:to="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_019f9ebc-8dbe-75de-bba7-8f783a96ef99_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PROPERTY AND EQUIPMENT</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ProceedsFromReverseRecapitalizationTransactionNet_019faf0c-8963-79d9-85cf-e8615dce76f5_terseLabel_en-US" xlink:label="lab_fac_ProceedsFromReverseRecapitalizationTransactionNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds received from reverse recapitalization and PIPE Financing, net of $20,064 of transaction costs</link:label>
    <link:label id="lab_fac_ProceedsFromReverseRecapitalizationTransactionNet_label_en-US" xlink:label="lab_fac_ProceedsFromReverseRecapitalizationTransactionNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Reverse Recapitalization Transaction, Net</link:label>
    <link:label id="lab_fac_ProceedsFromReverseRecapitalizationTransactionNet_documentation_en-US" xlink:label="lab_fac_ProceedsFromReverseRecapitalizationTransactionNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Reverse Recapitalization Transaction, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ProceedsFromReverseRecapitalizationTransactionNet" xlink:href="fac-20260630.xsd#fac_ProceedsFromReverseRecapitalizationTransactionNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ProceedsFromReverseRecapitalizationTransactionNet" xlink:to="lab_fac_ProceedsFromReverseRecapitalizationTransactionNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_019fa60c-7e20-7d3d-903c-3aefa9ae42ed_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash investing and financing activities:</link:label>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019f9eb7-cb82-708c-afbf-fa9a25f2b027_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_019fa60c-7e20-7846-950d-a2eda8a65418_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019fa60c-7e20-7236-876f-56c6577a2240_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
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    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_019fa5a6-3a6f-725c-8011-a842c09d0fbd_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019fb577-faf6-7ee8-b334-8d995c82f142_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_019fd26b-4aa2-7d37-8aa7-2360ad38a071_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic EPS:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019fb554-56c4-7bdc-9f44-9913a61d5105_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">STOCKHOLDERS' EQUITY</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_019fa5cd-d288-72c4-906e-4e980ddd9c5e_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_019fce61-67af-7d4c-a194-c52df7856216_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_019fce63-4a3e-7fc4-a79d-86ae2c31d3d3_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_019fca62-ede6-71b8-a802-c21c731fc7fb_verboseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Shares Outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Outstanding</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesOutstanding" xlink:to="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019f9eb7-cb83-7f8f-bd4f-d377de081840_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
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    <link:label id="lab_fac_PowerCoSEPowerCoMember_019faf8f-98c9-762e-aa47-e3a1a958ce56_terseLabel_en-US" xlink:label="lab_fac_PowerCoSEPowerCoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PowerCo SE (&#8220;PowerCo&#8221;)</link:label>
    <link:label id="lab_fac_PowerCoSEPowerCoMember_label_en-US" xlink:label="lab_fac_PowerCoSEPowerCoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PowerCo SE (&#8220;PowerCo&#8221;) [Member]</link:label>
    <link:label id="lab_fac_PowerCoSEPowerCoMember_documentation_en-US" xlink:label="lab_fac_PowerCoSEPowerCoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">PowerCo SE (&#8220;PowerCo&#8221;)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_PowerCoSEPowerCoMember" xlink:href="fac-20260630.xsd#fac_PowerCoSEPowerCoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_PowerCoSEPowerCoMember" xlink:to="lab_fac_PowerCoSEPowerCoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_019fb51f-2c0d-7bc2-87c6-3ca687d88a11_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Grants in period, weighted average exercise price (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice"/>
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    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems_019fd7e0-1261-7860-8464-b759f598c7a3_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems_label_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019fafc2-5e12-70a1-b4be-44f792b0ee8f_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_AccruedPrivateIssuanceLiabilityCurrent_019fecfd-6ace-78aa-8be8-c4fa9b7da129_terseLabel_en-US" xlink:label="lab_fac_AccruedPrivateIssuanceLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued private issuance liability</link:label>
    <link:label id="lab_fac_AccruedPrivateIssuanceLiabilityCurrent_label_en-US" xlink:label="lab_fac_AccruedPrivateIssuanceLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Private Issuance Liability, Current</link:label>
    <link:label id="lab_fac_AccruedPrivateIssuanceLiabilityCurrent_documentation_en-US" xlink:label="lab_fac_AccruedPrivateIssuanceLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Private Issuance Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_AccruedPrivateIssuanceLiabilityCurrent" xlink:href="fac-20260630.xsd#fac_AccruedPrivateIssuanceLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_AccruedPrivateIssuanceLiabilityCurrent" xlink:to="lab_fac_AccruedPrivateIssuanceLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_019fab5a-f4e6-7986-b863-9da0554b3627_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019fa5a6-3a6f-721e-aa89-e67964a80902_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019f9eb7-cb83-7bb2-a13b-fba778dd219e_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassBMember_019fa5dc-d836-758c-b169-f4fae5720ca7_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series B Common stock</link:label>
    <link:label id="lab_us-gaap_CommonClassBMember_label_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class B [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassBMember" xlink:to="lab_us-gaap_CommonClassBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_019fdc90-ddaf-729c-b1fb-2ded990c15c3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_019fa5b8-faf8-7a41-b229-53e9df27424f_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities, current portion</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_019fdc8b-4545-7822-8092-ff660bde2f39_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issued for services (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Issued for Services</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesIssuedForServices"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_019f9ebc-f387-7512-8451-7fb489ac7142_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendPaymentMember_019fafcc-03ec-77b5-8c63-44a17eb3a128_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendPaymentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected dividends</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendPaymentMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendPaymentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Dividend Payment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedDividendPaymentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputExpectedDividendPaymentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedDividendPaymentMember" xlink:to="lab_us-gaap_MeasurementInputExpectedDividendPaymentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019fa5eb-68d6-7fe5-b759-562a602368e9_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NET LOSS PER COMMON SHARE</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019f9eb7-cb83-79c8-8c99-4e22d56cf013_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019fa5a6-3a6f-753e-aefc-3ee0613ab408_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019f9eb7-cb83-75cb-bfdc-314eba2c65f0_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019fafc3-9d2f-7e26-8ad7-010c2a5a1062_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesA2RedeemableConvertiblePreferredStockMember_019fa5c7-b87c-7fb1-b400-70f633519d57_terseLabel_en-US" xlink:label="lab_fac_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-2 redeemable convertible preferred stock</link:label>
    <link:label id="lab_fac_SeriesA2RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_fac_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-2 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_fac_SeriesA2RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_fac_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-2 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:href="fac-20260630.xsd#fac_SeriesA2RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:to="lab_fac_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019fa60c-7e20-71ae-9fd5-027d39086666_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Property and equipment expenditures</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesACommonShareRedeemablePublicWarrantsMember_019fb527-f22a-703a-8702-bb425575df70_terseLabel_en-US" xlink:label="lab_fac_SeriesACommonShareRedeemablePublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Public Warrants</link:label>
    <link:label id="lab_fac_SeriesACommonShareRedeemablePublicWarrantsMember_label_en-US" xlink:label="lab_fac_SeriesACommonShareRedeemablePublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A Common Share Redeemable Public Warrants [Member]</link:label>
    <link:label id="lab_fac_SeriesACommonShareRedeemablePublicWarrantsMember_documentation_en-US" xlink:label="lab_fac_SeriesACommonShareRedeemablePublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A Common Share Redeemable Public Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesACommonShareRedeemablePublicWarrantsMember" xlink:href="fac-20260630.xsd#fac_SeriesACommonShareRedeemablePublicWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesACommonShareRedeemablePublicWarrantsMember" xlink:to="lab_fac_SeriesACommonShareRedeemablePublicWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_CollaborativeArrangementPrepayment_019fcaa4-5078-70fe-9ba6-3e8b660efd30_terseLabel_en-US" xlink:label="lab_fac_CollaborativeArrangementPrepayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepayments for services</link:label>
    <link:label id="lab_fac_CollaborativeArrangementPrepayment_label_en-US" xlink:label="lab_fac_CollaborativeArrangementPrepayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Prepayment</link:label>
    <link:label id="lab_fac_CollaborativeArrangementPrepayment_documentation_en-US" xlink:label="lab_fac_CollaborativeArrangementPrepayment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Prepayment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_CollaborativeArrangementPrepayment" xlink:href="fac-20260630.xsd#fac_CollaborativeArrangementPrepayment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_CollaborativeArrangementPrepayment" xlink:to="lab_fac_CollaborativeArrangementPrepayment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_019fd7e0-1261-792e-9b24-1abe6acdbec4_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_LegacyFactorialCommonStockShareholdersMember_019fd890-a7bd-70f1-b51d-8d96e228d851_terseLabel_en-US" xlink:label="lab_fac_LegacyFactorialCommonStockShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legacy Factorial Common Stock Shareholders</link:label>
    <link:label id="lab_fac_LegacyFactorialCommonStockShareholdersMember_label_en-US" xlink:label="lab_fac_LegacyFactorialCommonStockShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legacy Factorial Common Stock Shareholders [Member]</link:label>
    <link:label id="lab_fac_LegacyFactorialCommonStockShareholdersMember_documentation_en-US" xlink:label="lab_fac_LegacyFactorialCommonStockShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Legacy Factorial Common Stock Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_LegacyFactorialCommonStockShareholdersMember" xlink:href="fac-20260630.xsd#fac_LegacyFactorialCommonStockShareholdersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_LegacyFactorialCommonStockShareholdersMember" xlink:to="lab_fac_LegacyFactorialCommonStockShareholdersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_019fd26b-6d8f-78e3-9539-41f24e75a7fe_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted EPS:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDilutedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:to="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreference_019fa5cb-2bdd-7c41-94ae-c5b36a36f219_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, liquidation preference</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreference_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLiquidationPreference" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityLiquidationPreference"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLiquidationPreference" xlink:to="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays_019fcfa7-dbda-749d-9c2c-8034b1735157_terseLabel_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption, threshold trading days</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays_label_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Redemption, Threshold Trading Days</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays_documentation_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Redemption, Threshold Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays" xlink:href="fac-20260630.xsd#fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays" xlink:to="lab_fac_ClassOfWarrantOrRightRedemptionThresholdTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_LegacyFactorialPreferredStockShareholdersMember_019fd890-a7bd-7b7c-b51a-d0af5a2cb0c5_terseLabel_en-US" xlink:label="lab_fac_LegacyFactorialPreferredStockShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legacy Factorial Preferred Stock Shareholders</link:label>
    <link:label id="lab_fac_LegacyFactorialPreferredStockShareholdersMember_label_en-US" xlink:label="lab_fac_LegacyFactorialPreferredStockShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legacy Factorial Preferred Stock Shareholders [Member]</link:label>
    <link:label id="lab_fac_LegacyFactorialPreferredStockShareholdersMember_documentation_en-US" xlink:label="lab_fac_LegacyFactorialPreferredStockShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Legacy Factorial Preferred Stock Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_LegacyFactorialPreferredStockShareholdersMember" xlink:href="fac-20260630.xsd#fac_LegacyFactorialPreferredStockShareholdersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_LegacyFactorialPreferredStockShareholdersMember" xlink:to="lab_fac_LegacyFactorialPreferredStockShareholdersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019fa60c-7e20-7536-9335-242b3b377fed_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_MercedesBenzMember_019fca9e-3cdd-77d0-8a93-bf37ac2aed0a_terseLabel_en-US" xlink:label="lab_fac_MercedesBenzMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mercedes-Benz</link:label>
    <link:label id="lab_fac_MercedesBenzMember_label_en-US" xlink:label="lab_fac_MercedesBenzMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mercedes-Benz [Member]</link:label>
    <link:label id="lab_fac_MercedesBenzMember_documentation_en-US" xlink:label="lab_fac_MercedesBenzMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mercedes-Benz</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_MercedesBenzMember" xlink:href="fac-20260630.xsd#fac_MercedesBenzMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_MercedesBenzMember" xlink:to="lab_fac_MercedesBenzMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtPolicyTextBlock_019faf1f-2c58-7f7b-a4d8-2ca940ef0260_terseLabel_en-US" xlink:label="lab_us-gaap_DebtPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Promissory Notes, Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtPolicyTextBlock" xlink:to="lab_us-gaap_DebtPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherReceivablesNetCurrent_019fcf76-8936-7f73-9ee2-609b6257872f_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Receivables under collaboration agreements (includes $0 and $1,000 as related party as of June 30, 2026, and December 31, 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_OtherReceivablesNetCurrent_019fca9e-a651-77d3-aacd-bbb2299b20f4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables under collaboration agreements</link:label>
    <link:label id="lab_us-gaap_OtherReceivablesNetCurrent_label_en-US" xlink:label="lab_us-gaap_OtherReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Receivables, Net, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherReceivablesNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherReceivablesNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherReceivablesNetCurrent" xlink:to="lab_us-gaap_OtherReceivablesNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019fa5eb-68d6-7601-90fb-2fa22293ba95_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average common stock outstanding - diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019fd282-8e87-76c6-a4cb-a1734f8fc3e3_totalLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Weighted average diluted shares of common stock outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019f9eb7-cb83-7e55-8d1f-a1e06005b759_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_019fca9e-3cdd-7407-b1dc-0a1155334433_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:to="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_019f9ec2-433f-74ea-bd51-cf788a14548e_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, after Accumulated Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TypeOfArrangementAxis_019faf8f-98c9-78e7-ad82-bde0246f3524_terseLabel_en-US" xlink:label="lab_us-gaap_TypeOfArrangementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
    <link:label id="lab_us-gaap_TypeOfArrangementAxis_label_en-US" xlink:label="lab_us-gaap_TypeOfArrangementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TypeOfArrangementAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TypeOfArrangementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TypeOfArrangementAxis" xlink:to="lab_us-gaap_TypeOfArrangementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization_019fce55-23a8-7409-8934-420019c076ee_terseLabel_en-US" xlink:label="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock in connection with reverse recapitalization and PIPE Financing, net of issuance costs (in shares)</link:label>
    <link:label id="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization_019fd8ad-d1da-7ce1-a561-b46fc3c2390b_verboseLabel_en-US" xlink:label="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total (in shares)</link:label>
    <link:label id="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization_label_en-US" xlink:label="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Reverse Recapitalization</link:label>
    <link:label id="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization_documentation_en-US" xlink:label="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:href="fac-20260630.xsd#fac_StockIssuedDuringPeriodSharesReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:to="lab_fac_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019fab7c-3775-77c3-b999-7c881e83cebb_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SiyuHuangMember_label_en-US" xlink:label="lab_fac_SiyuHuangMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Siyu Huang [Member]</link:label>
    <link:label id="lab_fac_SiyuHuangMember_documentation_en-US" xlink:label="lab_fac_SiyuHuangMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Siyu Huang</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SiyuHuangMember" xlink:href="fac-20260630.xsd#fac_SiyuHuangMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SiyuHuangMember" xlink:to="lab_fac_SiyuHuangMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_019fa617-0261-73eb-8bf5-8ee3f5d01528_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other non-current assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Noncurrent Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredChargesPolicyTextBlock_019faf1e-6be7-7a48-b988-5c4a937ff552_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredChargesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Transaction Costs</link:label>
    <link:label id="lab_us-gaap_DeferredChargesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DeferredChargesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Charges, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredChargesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredChargesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredChargesPolicyTextBlock" xlink:to="lab_us-gaap_DeferredChargesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization_019f9ec2-034e-7ebd-b1d5-bb90c58f1d8f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated depreciation</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, Accumulated Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAccumulatedDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio_019fca39-7d5c-7c25-9b4b-5ce48e3d435f_terseLabel_en-US" xlink:label="lab_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Converted instrument, issued prior to exchange ratio (in shares)</link:label>
    <link:label id="lab_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio_label_en-US" xlink:label="lab_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Converted Instrument, Shares Issued, Prior To Exchange Ratio</link:label>
    <link:label id="lab_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio_documentation_en-US" xlink:label="lab_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Conversion, Converted Instrument, Shares Issued, Prior To Exchange Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio" xlink:href="fac-20260630.xsd#fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio" xlink:to="lab_fac_DebtConversionConvertedInstrumentSharesIssuedPriorToExchangeRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_AlexYuMember_label_en-US" xlink:label="lab_fac_AlexYuMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Alex Yu [Member]</link:label>
    <link:label id="lab_fac_AlexYuMember_documentation_en-US" xlink:label="lab_fac_AlexYuMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Alex Yu</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_AlexYuMember" xlink:href="fac-20260630.xsd#fac_AlexYuMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_AlexYuMember" xlink:to="lab_fac_AlexYuMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_019fce49-e0f5-788d-8c95-762fa4a8e80c_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock based compensation</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019fab59-ec1f-7015-ba08-77120f66719c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExercisePriceMember_019fafc4-f190-738e-ac2b-791d2ed9d8ee_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Strike price</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExercisePriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Exercise Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExercisePriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputExercisePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExercisePriceMember" xlink:to="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts_019fed17-901c-7d1b-9072-a3849f88896a_negatedTerseLabel_en-US" xlink:label="lab_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deferred transaction costs paid</link:label>
    <link:label id="lab_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts_label_en-US" xlink:label="lab_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Deferred Reverse Recapitalization Transaction Costs</link:label>
    <link:label id="lab_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts_documentation_en-US" xlink:label="lab_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments of Deferred Reverse Recapitalization Transaction Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts" xlink:href="fac-20260630.xsd#fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts" xlink:to="lab_fac_PaymentsOfDeferredReverseRecapitalizationTransactionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants_019fd273-ef50-717c-83d0-90b3a956cb26_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dilutive effect of warrants - treasury stock method</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Call Options and Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:to="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_CollaborativeArrangementTerm_019faf8f-98c9-7ce4-a125-e4525e3086fc_terseLabel_en-US" xlink:label="lab_fac_CollaborativeArrangementTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative agreement term</link:label>
    <link:label id="lab_fac_CollaborativeArrangementTerm_label_en-US" xlink:label="lab_fac_CollaborativeArrangementTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Term</link:label>
    <link:label id="lab_fac_CollaborativeArrangementTerm_documentation_en-US" xlink:label="lab_fac_CollaborativeArrangementTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_CollaborativeArrangementTerm" xlink:href="fac-20260630.xsd#fac_CollaborativeArrangementTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_CollaborativeArrangementTerm" xlink:to="lab_fac_CollaborativeArrangementTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019fafc2-5e12-7547-8e36-c4d9e5357432_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_019fa60c-7e20-76ba-baf3-b886fbfe0a88_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_019fa5a6-3a6f-7770-bd51-83fc8be54efc_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in usd per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightLineItems_019fcf9d-3f62-7ce7-9a86-eba5cb01c373_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:type="arc" order="1"/>
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    <link:label id="lab_fac_DebtInstrumentConvertibleThresholdProceedsFromConvertibleDebt_label_en-US" xlink:label="lab_fac_DebtInstrumentConvertibleThresholdProceedsFromConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible, Threshold Proceeds from Convertible Debt</link:label>
    <link:label id="lab_fac_DebtInstrumentConvertibleThresholdProceedsFromConvertibleDebt_documentation_en-US" xlink:label="lab_fac_DebtInstrumentConvertibleThresholdProceedsFromConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible, Threshold Proceeds from Convertible Debt</link:label>
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    <link:label id="lab_us-gaap_TemporaryEquityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityTableTextBlock"/>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019fafe8-542c-76cf-b080-31a6e804f8cf_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_019fafa8-e21e-761c-8786-48ea654a845e_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightAxis"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_fac_CantorAdvisorMember" xlink:href="fac-20260630.xsd#fac_CantorAdvisorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_CantorAdvisorMember" xlink:to="lab_fac_CantorAdvisorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingMember_019f9ec2-034e-7e30-9395-9966215b6719_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Buildings</link:label>
    <link:label id="lab_us-gaap_BuildingMember_label_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingMember" xlink:to="lab_us-gaap_BuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_RestrictedCashFairValueDisclosure_019fab59-ec1f-707b-a3c8-90a822150bca_terseLabel_en-US" xlink:label="lab_fac_RestrictedCashFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Money market (included in restricted cash)</link:label>
    <link:label id="lab_fac_RestrictedCashFairValueDisclosure_label_en-US" xlink:label="lab_fac_RestrictedCashFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash, Fair Value Disclosure</link:label>
    <link:label id="lab_fac_RestrictedCashFairValueDisclosure_documentation_en-US" xlink:label="lab_fac_RestrictedCashFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_RestrictedCashFairValueDisclosure" xlink:href="fac-20260630.xsd#fac_RestrictedCashFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_RestrictedCashFairValueDisclosure" xlink:to="lab_fac_RestrictedCashFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_019fed02-cbf8-72d5-90e8-eaa33f0c6f91_terseLabel_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonrelated Party</link:label>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonrelated Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonrelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonrelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonrelatedPartyMember" xlink:to="lab_us-gaap_NonrelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification_019fab6e-9911-7694-85f6-7edf46742c84_terseLabel_en-US" xlink:label="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification of Warrant liability&#160;for Series A Common Stock&#160;from equity to liability</link:label>
    <link:label id="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification_label_en-US" xlink:label="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Reclassification</link:label>
    <link:label id="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification_documentation_en-US" xlink:label="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Reclassification</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification" xlink:href="fac-20260630.xsd#fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification" xlink:to="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityReclassification" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertibleDebtFairValueDisclosures_019fab62-14fa-752b-8759-cf03dee90bfb_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertibleDebtFairValueDisclosures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible promissory notes &#8211; related parties</link:label>
    <link:label id="lab_us-gaap_ConvertibleDebtFairValueDisclosures_label_en-US" xlink:label="lab_us-gaap_ConvertibleDebtFairValueDisclosures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Debt, Fair Value Disclosures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertibleDebtFairValueDisclosures" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtFairValueDisclosures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertibleDebtFairValueDisclosures" xlink:to="lab_us-gaap_ConvertibleDebtFairValueDisclosures" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019fa5a6-3a6f-7f51-97d1-a91f30b953bc_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_019fa5eb-68d6-7be8-8f50-ea2916266aa4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_019faf0c-8963-7c8f-8cc8-83dafe9b7735_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issued and sold (in shares)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019fa60c-7e20-7299-8464-b8077780de42_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_019fa590-474e-7363-bbd5-3eef91e3e412_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019fca85-8858-71c5-99b7-1b71ecda057a_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_019fb51f-2c0d-7e91-ba5f-76a8f9b980a6_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation costs</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_TemporaryEquityValueConversionOfConvertibleSecurities_019fce53-0b8f-765e-8720-27e36045aab0_negatedTerseLabel_en-US" xlink:label="lab_fac_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Conversion of redeemable convertible preferred stock into Series A Common Stock</link:label>
    <link:label id="lab_fac_TemporaryEquityValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_fac_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Value, Conversion of Convertible Securities</link:label>
    <link:label id="lab_fac_TemporaryEquityValueConversionOfConvertibleSecurities_documentation_en-US" xlink:label="lab_fac_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Value, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:href="fac-20260630.xsd#fac_TemporaryEquityValueConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:to="lab_fac_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_019f9eb7-cb82-7242-9246-0d42553bfe2f_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_us-gaap_SegmentDomain_019fdc9c-f0d4-7494-9a51-5578f134ffa3_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityLineItems_019fca62-c918-7297-95f2-1b1b1cf36cc3_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLineItems_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLineItems" xlink:to="lab_us-gaap_TemporaryEquityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019fb57a-6d24-7e50-8fba-7a42f33ff3ab_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CONVERTIBLE PROMISSORY NOTES &#8212; RELATED PARTIES</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019fb57d-dcd8-7055-8df9-717aa2a0a3dd_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">CONVERTIBLE PROMISSORY NOTES</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherReceivables_019fd28e-2d3e-7a7c-879e-49f075bc638f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Receivables under collaboration agreements</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherReceivables_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019fce46-7c68-795d-a4e5-d608fc0ca950_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_019fafc2-22c8-7432-8f9b-ccc22211bc58_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_019faf0c-8963-756f-ae8b-73419d95b8c1_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from shares issued and sold</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold_019fcfa1-30c0-7ed9-a165-57097dcbe8df_terseLabel_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption, exercise price threshold (in usd per share)</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold_label_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption, Exercise Price of Warrants or Rights, Threshold</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold_documentation_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption, Exercise Price of Warrants or Rights, Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold" xlink:href="fac-20260630.xsd#fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold" xlink:to="lab_fac_ClassOfWarrantOrRightRedemptionExercisePriceOfWarrantsOrRightsThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019fb57c-8709-74cd-ada9-ed15859c420b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate (in percent)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_019faf8f-98c9-7e5c-aae7-9bada5279a52_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019fa5a6-3a6f-7829-8c74-fa2f63781087_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; equity (deficit)</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019fce66-161b-79e1-9de7-a710c83fa080_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019fce66-3271-77ed-bd9b-4f5ad1a42ced_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_019fcfc9-4ac2-7b6b-9f2d-8481fdf583af_totalLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other income (expenses), net</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_019fcfc7-862f-720d-9c5d-12d79a8c4e48_terseLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total other income (expenses), net</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpense" xlink:to="lab_us-gaap_NonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_CommonStockVotingRightsNumberOfVotes_019fb562-defc-7b1a-a785-74f7d8588db5_terseLabel_en-US" xlink:label="lab_fac_CommonStockVotingRightsNumberOfVotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Voting rights, number of votes</link:label>
    <link:label id="lab_fac_CommonStockVotingRightsNumberOfVotes_label_en-US" xlink:label="lab_fac_CommonStockVotingRightsNumberOfVotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Voting Rights, Number Of Votes</link:label>
    <link:label id="lab_fac_CommonStockVotingRightsNumberOfVotes_documentation_en-US" xlink:label="lab_fac_CommonStockVotingRightsNumberOfVotes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Voting Rights, Number Of Votes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_CommonStockVotingRightsNumberOfVotes" xlink:href="fac-20260630.xsd#fac_CommonStockVotingRightsNumberOfVotes"/>
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    <link:label id="lab_us-gaap_AssetsAbstract_019fa5a6-3a6f-7e0f-8e66-48a1ac5c0494_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS:</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_CartesianGrowthCorporationCGCMember_019fd88d-b3cc-79a9-b88a-df53472ce017_terseLabel_en-US" xlink:label="lab_fac_CartesianGrowthCorporationCGCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cartesian Growth Corporation (&#8220;CGC&#8221;)</link:label>
    <link:label id="lab_fac_CartesianGrowthCorporationCGCMember_label_en-US" xlink:label="lab_fac_CartesianGrowthCorporationCGCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cartesian Growth Corporation (&#8220;CGC&#8221;) [Member]</link:label>
    <link:label id="lab_fac_CartesianGrowthCorporationCGCMember_documentation_en-US" xlink:label="lab_fac_CartesianGrowthCorporationCGCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cartesian Growth Corporation (&#8220;CGC&#8221;)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_CartesianGrowthCorporationCGCMember" xlink:href="fac-20260630.xsd#fac_CartesianGrowthCorporationCGCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_CartesianGrowthCorporationCGCMember" xlink:to="lab_fac_CartesianGrowthCorporationCGCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment_019fa61c-b9de-78f8-a482-87084915a490_negatedTerseLabel_en-US" xlink:label="lab_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Advances on property and equipment</link:label>
    <link:label id="lab_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment_label_en-US" xlink:label="lab_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For Advances On Property, Plant, and Equipment</link:label>
    <link:label id="lab_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment_documentation_en-US" xlink:label="lab_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments For Advances On Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment" xlink:href="fac-20260630.xsd#fac_PaymentsForAdvancesOnPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment" xlink:to="lab_fac_PaymentsForAdvancesOnPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfessionalFees_019fca85-8858-71aa-8e80-a85d27c8fea6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Professional service expense</link:label>
    <link:label id="lab_us-gaap_ProfessionalFees_label_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Professional Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfessionalFees" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfessionalFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfessionalFees" xlink:to="lab_us-gaap_ProfessionalFees" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_019f9ed0-afa8-7d4e-b4f9-c968f6590283_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ACCRUED EXPENSES</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019fa5a6-3a6f-72ed-ba65-6f89befeb622_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other current assets (includes $720 and $1,110 as related party as of June 30, 2026, and December 31, 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019fa5e6-2370-7beb-a6bd-a787dc951ed7_verboseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other current assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:to="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019fab70-e2ca-7d1a-ac56-b8441271bd57_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_019fcfc6-a5cf-7efa-8882-aaad2fd1f7aa_negatedLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Selling, general and administrative (includes $65 and $44 for the three months ended June 30, 2026 and 2025, respectively; and $153 and $88 for the six months ended June 30, 2026 and 2025, respectively, of related party expenses)</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_019fa591-3283-70ce-b22b-4a441dd65b46_terseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling, general and administrative</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SellingGeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrivatePlacementMember_019fd7e0-1261-7e6c-b453-f62215055962_terseLabel_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Placement</link:label>
    <link:label id="lab_us-gaap_PrivatePlacementMember_label_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivatePlacementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrivatePlacementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrivatePlacementMember" xlink:to="lab_us-gaap_PrivatePlacementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember_019fd890-a7bd-7931-8379-07462b74010b_terseLabel_en-US" xlink:label="lab_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cartesian Growth Corporation (&#8220;CGC&#8221;) Series A Shares (&#8220;NRA Shares&#8221;)</link:label>
    <link:label id="lab_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember_label_en-US" xlink:label="lab_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cartesian Growth Corporation (&#8220;CGC&#8221;) Series A Shares (&#8220;NRA Shares&#8221;) [Member]</link:label>
    <link:label id="lab_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember_documentation_en-US" xlink:label="lab_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cartesian Growth Corporation (&#8220;CGC&#8221;) Series A Shares (&#8220;NRA Shares&#8221;)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember" xlink:href="fac-20260630.xsd#fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember" xlink:to="lab_fac_CartesianGrowthCorporationCGCSeriesASharesNRASharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019fb567-101c-7e45-babe-c5316b4c4cf6_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">COMMITMENTS AND CONTINGENCIES</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019fca89-7b1e-773a-96ba-00159811e7aa_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_019fa5eb-68d6-7033-880b-4f63d9221bec_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Anti-dilutive securities</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_019fa5eb-68d6-766d-b322-b6963947d6b2_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock units</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_019fa5eb-68d6-728f-93e3-7e2145546e74_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019f9eb7-cb83-7f4e-8892-eef8e398ecc7_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019fa60c-7e20-744f-8e00-a3d4e3b12911_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesDRedeemableConvertiblePreferredStockMember_019fa5c8-cb91-73b6-a910-acba27f36a1d_terseLabel_en-US" xlink:label="lab_fac_SeriesDRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D redeemable convertible preferred stock</link:label>
    <link:label id="lab_fac_SeriesDRedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_fac_SeriesDRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_fac_SeriesDRedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_fac_SeriesDRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series D Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesDRedeemableConvertiblePreferredStockMember" xlink:href="fac-20260630.xsd#fac_SeriesDRedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesDRedeemableConvertiblePreferredStockMember" xlink:to="lab_fac_SeriesDRedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_019fa5a6-3a6f-74ca-9ac1-a8d0bb4aa9d1_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders&#8217; equity (deficit):</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019f9eb7-cb82-7d6d-832d-b4093c03eec8_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019fab59-ec1f-7947-95aa-aad3fb7d1812_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration_019fca51-109d-7a63-b5d9-60bbdf2eabad_terseLabel_en-US" xlink:label="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum consideration</link:label>
    <link:label id="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration_label_en-US" xlink:label="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Rights and Obligations, Maximum Consideration</link:label>
    <link:label id="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration_documentation_en-US" xlink:label="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Rights and Obligations, Maximum Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration" xlink:href="fac-20260630.xsd#fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration" xlink:to="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumConsideration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019fa58a-7c35-767e-af12-0578dabf1cbb_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ReverseRecapitalizationAbstract_label_en-US" xlink:label="lab_fac_ReverseRecapitalizationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization [Abstract]</link:label>
    <link:label id="lab_fac_ReverseRecapitalizationAbstract_documentation_en-US" xlink:label="lab_fac_ReverseRecapitalizationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ReverseRecapitalizationAbstract" xlink:href="fac-20260630.xsd#fac_ReverseRecapitalizationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ReverseRecapitalizationAbstract" xlink:to="lab_fac_ReverseRecapitalizationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_NoncashLeaseExpenseAndAmortization_019fa610-c0c4-7111-9f12-082be62d74fe_terseLabel_en-US" xlink:label="lab_fac_NoncashLeaseExpenseAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash lease expenses and amortization</link:label>
    <link:label id="lab_fac_NoncashLeaseExpenseAndAmortization_label_en-US" xlink:label="lab_fac_NoncashLeaseExpenseAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Lease Expense And Amortization</link:label>
    <link:label id="lab_fac_NoncashLeaseExpenseAndAmortization_documentation_en-US" xlink:label="lab_fac_NoncashLeaseExpenseAndAmortization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncash Lease Expense And Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_NoncashLeaseExpenseAndAmortization" xlink:href="fac-20260630.xsd#fac_NoncashLeaseExpenseAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_NoncashLeaseExpenseAndAmortization" xlink:to="lab_fac_NoncashLeaseExpenseAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019f9eb7-cb83-7d76-a768-88ef166c9dba_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019fce46-7c68-75ef-a86c-b24c5fbe54ca_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_019fb53e-0d3c-7a62-91b2-1b5b2e8c5bd7_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_019fcaa8-31c2-7b52-bedb-5d309c4c3d57_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SUBSEQUENT EVENTS</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_019fafca-76bd-7b5f-95a5-0c7018c07984_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed volatility</link:label>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Price Volatility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputPriceVolatilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:to="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ValuationTechniqueSPACExitScenarioMember_019fafc3-4dd1-7423-be0f-66b172468b4c_terseLabel_en-US" xlink:label="lab_fac_ValuationTechniqueSPACExitScenarioMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Technique, SPAC Exit Scenario</link:label>
    <link:label id="lab_fac_ValuationTechniqueSPACExitScenarioMember_label_en-US" xlink:label="lab_fac_ValuationTechniqueSPACExitScenarioMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, SPAC Exit Scenario [Member]</link:label>
    <link:label id="lab_fac_ValuationTechniqueSPACExitScenarioMember_documentation_en-US" xlink:label="lab_fac_ValuationTechniqueSPACExitScenarioMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, SPAC Exit Scenario</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ValuationTechniqueSPACExitScenarioMember" xlink:href="fac-20260630.xsd#fac_ValuationTechniqueSPACExitScenarioMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ValuationTechniqueSPACExitScenarioMember" xlink:to="lab_fac_ValuationTechniqueSPACExitScenarioMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_StockIssuanceCostsIncludedInAccruedLiabilities_019fa64d-9dd3-7773-89c5-6cd7ab2c0203_terseLabel_en-US" xlink:label="lab_fac_StockIssuanceCostsIncludedInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred transaction costs included in accrued expenses</link:label>
    <link:label id="lab_fac_StockIssuanceCostsIncludedInAccruedLiabilities_label_en-US" xlink:label="lab_fac_StockIssuanceCostsIncludedInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issuance Costs Included In Accrued Liabilities</link:label>
    <link:label id="lab_fac_StockIssuanceCostsIncludedInAccruedLiabilities_documentation_en-US" xlink:label="lab_fac_StockIssuanceCostsIncludedInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issuance Costs Included In Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_StockIssuanceCostsIncludedInAccruedLiabilities" xlink:href="fac-20260630.xsd#fac_StockIssuanceCostsIncludedInAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_StockIssuanceCostsIncludedInAccruedLiabilities" xlink:to="lab_fac_StockIssuanceCostsIncludedInAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember_019fafb3-ddc6-7807-9f85-011ae0302f79_terseLabel_en-US" xlink:label="lab_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D</link:label>
    <link:label id="lab_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember_label_en-US" xlink:label="lab_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Redeemable Convertible Preferred Stock Warrant [Member]</link:label>
    <link:label id="lab_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember_documentation_en-US" xlink:label="lab_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series D Redeemable Convertible Preferred Stock Warrant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember" xlink:href="fac-20260630.xsd#fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember" xlink:to="lab_fac_SeriesDRedeemableConvertiblePreferredStockWarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_019fb51f-2c0d-78d2-8789-4b6596759efb_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation costs, weighted-average period</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioPreviouslyReportedMember_019fce46-7c68-75be-b55f-e7666e32452c_terseLabel_en-US" xlink:label="lab_srt_ScenarioPreviouslyReportedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Previously Reported</link:label>
    <link:label id="lab_srt_ScenarioPreviouslyReportedMember_label_en-US" xlink:label="lab_srt_ScenarioPreviouslyReportedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Previously Reported [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioPreviouslyReportedMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioPreviouslyReportedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioPreviouslyReportedMember" xlink:to="lab_srt_ScenarioPreviouslyReportedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019fa590-474e-7475-af82-0c26adb88c8a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019fa5a6-3a6f-7423-9b55-0f606da6b125_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019fd7ee-938a-71dd-b734-4c190f2a8e77_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_019fa5a6-3a6f-7179-bb9b-67754f76d3cc_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertibleDebtMember_019fab6e-9911-7815-b7ae-5c66a43f5768_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertibleDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Promissory Notes</link:label>
    <link:label id="lab_us-gaap_ConvertibleDebtMember_label_en-US" xlink:label="lab_us-gaap_ConvertibleDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertibleDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertibleDebtMember" xlink:to="lab_us-gaap_ConvertibleDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalLeaseObligationsIncurred_019fa63c-3f37-7a43-84ef-7282e9646246_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalLeaseObligationsIncurred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_CapitalLeaseObligationsIncurred_label_en-US" xlink:label="lab_us-gaap_CapitalLeaseObligationsIncurred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Obligation Incurred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalLeaseObligationsIncurred" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CapitalLeaseObligationsIncurred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalLeaseObligationsIncurred" xlink:to="lab_us-gaap_CapitalLeaseObligationsIncurred" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember_019fafb3-9fda-795d-935a-eb6a37f92026_terseLabel_en-US" xlink:label="lab_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series B-1</link:label>
    <link:label id="lab_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember_label_en-US" xlink:label="lab_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series B-1 Redeemable Convertible Preferred Stock Warrant [Member]</link:label>
    <link:label id="lab_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember_documentation_en-US" xlink:label="lab_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series B-1 Redeemable Convertible Preferred Stock Warrant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember" xlink:href="fac-20260630.xsd#fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember" xlink:to="lab_fac_SeriesB1RedeemableConvertiblePreferredStockWarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure_019fdca8-ab45-75f0-a68e-58f165f7a4ef_terseLabel_en-US" xlink:label="lab_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued private issuance liability (included in accrued expenses)</link:label>
    <link:label id="lab_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure_label_en-US" xlink:label="lab_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Private Issuance Liability, Fair Value Disclosure</link:label>
    <link:label id="lab_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure_documentation_en-US" xlink:label="lab_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Private Issuance Liability, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure" xlink:href="fac-20260630.xsd#fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure" xlink:to="lab_fac_AccruedPrivateIssuanceLiabilityFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_019fb51f-2c0d-7854-b8c3-e552aab8612b_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Grants in period, weighted average grant-date fair value (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_019fab79-d8ae-7a25-a94d-9947603ff064_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">STOCK BASED COMPENSATION</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019fab6f-37d6-79e8-a303-aab887662d06_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromConvertibleDebt_019fa62a-7dcd-79e5-9718-506c3d69f548_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of convertible promissory notes, net</link:label>
    <link:label id="lab_us-gaap_ProceedsFromConvertibleDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Convertible Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromConvertibleDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromConvertibleDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromConvertibleDebt" xlink:to="lab_us-gaap_ProceedsFromConvertibleDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OccupancyNet_019fca85-8858-7449-995d-473b7476ec8e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OccupancyNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Occupancy expense</link:label>
    <link:label id="lab_us-gaap_OccupancyNet_label_en-US" xlink:label="lab_us-gaap_OccupancyNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Occupancy, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OccupancyNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OccupancyNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OccupancyNet" xlink:to="lab_us-gaap_OccupancyNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019fab7c-4d4f-7772-8221-3331f4c684b2_verboseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_DebtInstrumentConvertibleTermsOfConversionDomain_019fca19-9a18-78c0-8247-bcb6932366cb_terseLabel_en-US" xlink:label="lab_fac_DebtInstrumentConvertibleTermsOfConversionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible Terms Of Conversion [Domain]</link:label>
    <link:label id="lab_fac_DebtInstrumentConvertibleTermsOfConversionDomain_label_en-US" xlink:label="lab_fac_DebtInstrumentConvertibleTermsOfConversionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible Terms Of Conversion [Domain]</link:label>
    <link:label id="lab_fac_DebtInstrumentConvertibleTermsOfConversionDomain_documentation_en-US" xlink:label="lab_fac_DebtInstrumentConvertibleTermsOfConversionDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible Terms Of Conversion [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_DebtInstrumentConvertibleTermsOfConversionDomain" xlink:href="fac-20260630.xsd#fac_DebtInstrumentConvertibleTermsOfConversionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_DebtInstrumentConvertibleTermsOfConversionDomain" xlink:to="lab_fac_DebtInstrumentConvertibleTermsOfConversionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_019fd87e-bd22-787c-baab-c5b3ad9a93a6_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Series A common stock from stock option exercises (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_019fafc8-9ac3-73f2-b7d1-180956b56cbe_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_019fed01-190a-7f64-8cc5-db81873d3647_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019fce46-7c68-706f-99e2-654f4311dfec_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_019fa5a6-3a6f-7365-8f7a-46ce3c81a8cf_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities, net of current portion</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_019fecfa-8f27-772d-8d01-2b510b2ec247_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total operating expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementDomain_019fce46-7c68-7805-8f4b-e413a20367af_terseLabel_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
    <link:label id="lab_srt_RestatementDomain_label_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementDomain" xlink:to="lab_srt_RestatementDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_019f9ec2-034e-7df8-90d7-f26749d211ba_terseLabel_en-US" xlink:label="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Computer and software</link:label>
    <link:label id="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_label_en-US" xlink:label="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software, In-Development, Internally Developed, and Purchased [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SoftwareAndSoftwareDevelopmentCostsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:to="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_WarrantsPolicyPolicyTextBlock_019fdc89-b9a0-798d-b017-5c303ef7d8c2_terseLabel_en-US" xlink:label="lab_fac_WarrantsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant Instruments</link:label>
    <link:label id="lab_fac_WarrantsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_fac_WarrantsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants, Policy [Policy Text Block]</link:label>
    <link:label id="lab_fac_WarrantsPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_fac_WarrantsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants, Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_WarrantsPolicyPolicyTextBlock" xlink:href="fac-20260630.xsd#fac_WarrantsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_WarrantsPolicyPolicyTextBlock" xlink:to="lab_fac_WarrantsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019fce65-38aa-7f2d-8669-2369a62286b1_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019fa5a6-3a6f-71e5-973d-bdc1059e6815_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ff1f5-e6df-74b2-8983-90c803c0a8aa_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ff1f5-d277-7aeb-978b-4ef86da7ed82_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SaleOfStockNumberOfSharesIssuableInTransaction_019fd7e0-1261-7c64-8b03-040df54d5c1c_terseLabel_en-US" xlink:label="lab_fac_SaleOfStockNumberOfSharesIssuableInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, issuable in transaction (in shares)</link:label>
    <link:label id="lab_fac_SaleOfStockNumberOfSharesIssuableInTransaction_label_en-US" xlink:label="lab_fac_SaleOfStockNumberOfSharesIssuableInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issuable in Transaction</link:label>
    <link:label id="lab_fac_SaleOfStockNumberOfSharesIssuableInTransaction_documentation_en-US" xlink:label="lab_fac_SaleOfStockNumberOfSharesIssuableInTransaction" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issuable in Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SaleOfStockNumberOfSharesIssuableInTransaction" xlink:href="fac-20260630.xsd#fac_SaleOfStockNumberOfSharesIssuableInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SaleOfStockNumberOfSharesIssuableInTransaction" xlink:to="lab_fac_SaleOfStockNumberOfSharesIssuableInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019fa5eb-68d6-7a4e-9390-53b2c80bcf3d_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss per share attributable to common stockholders &#8211; diluted (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019fd283-f15d-7936-8190-5093f4755b70_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted loss per share (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019f9eb7-cb83-73f6-9d0b-a2cce8a361c9_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollaborativeArrangementTransactionWithPartyToCollaborativeArrangementMember_019faf8f-98c9-7e53-8efe-ab0d7f04c462_terseLabel_en-US" xlink:label="lab_us-gaap_CollaborativeArrangementTransactionWithPartyToCollaborativeArrangementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Transaction with Party to Collaborative Arrangement</link:label>
    <link:label id="lab_us-gaap_CollaborativeArrangementTransactionWithPartyToCollaborativeArrangementMember_label_en-US" xlink:label="lab_us-gaap_CollaborativeArrangementTransactionWithPartyToCollaborativeArrangementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Transaction with Party to Collaborative Arrangement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollaborativeArrangementTransactionWithPartyToCollaborativeArrangementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CollaborativeArrangementTransactionWithPartyToCollaborativeArrangementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollaborativeArrangementTransactionWithPartyToCollaborativeArrangementMember" xlink:to="lab_us-gaap_CollaborativeArrangementTransactionWithPartyToCollaborativeArrangementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019fa60c-7e20-7716-8d95-434ce3b4dc21_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_LetterAgreementMember_019fd890-a7bd-7d0f-a3a1-d9b4a0a0d7de_terseLabel_en-US" xlink:label="lab_fac_LetterAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letter Agreement</link:label>
    <link:label id="lab_fac_LetterAgreementMember_label_en-US" xlink:label="lab_fac_LetterAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letter Agreement [Member]</link:label>
    <link:label id="lab_fac_LetterAgreementMember_documentation_en-US" xlink:label="lab_fac_LetterAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Letter Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_LetterAgreementMember" xlink:href="fac-20260630.xsd#fac_LetterAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_LetterAgreementMember" xlink:to="lab_fac_LetterAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_019fa60c-7e20-722d-a085-6e5f403c6ed4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other current assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_019fab5b-7a06-7dfb-930a-2d4c919f4767_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays_019fcfa1-30c0-7964-adf4-aef7b76de9b5_terseLabel_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption, threshold consecutive trading days</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays_label_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Redemption, Threshold Consecutive Trading Days</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays_documentation_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Redemption, Threshold Consecutive Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays" xlink:href="fac-20260630.xsd#fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays" xlink:to="lab_fac_ClassOfWarrantOrRightRedemptionThresholdConsecutiveTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SponsorMembersMember_019fd890-a7bd-7a8c-8266-ec75ee61c21a_terseLabel_en-US" xlink:label="lab_fac_SponsorMembersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sponsor Members</link:label>
    <link:label id="lab_fac_SponsorMembersMember_label_en-US" xlink:label="lab_fac_SponsorMembersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sponsor Members [Member]</link:label>
    <link:label id="lab_fac_SponsorMembersMember_documentation_en-US" xlink:label="lab_fac_SponsorMembersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sponsor Members</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SponsorMembersMember" xlink:href="fac-20260630.xsd#fac_SponsorMembersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SponsorMembersMember" xlink:to="lab_fac_SponsorMembersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_AdvisoryAgreementTerm_019fd7e0-1261-70ba-a206-aba83a912f70_terseLabel_en-US" xlink:label="lab_fac_AdvisoryAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advisory agreement term</link:label>
    <link:label id="lab_fac_AdvisoryAgreementTerm_label_en-US" xlink:label="lab_fac_AdvisoryAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advisory Agreement, Term</link:label>
    <link:label id="lab_fac_AdvisoryAgreementTerm_documentation_en-US" xlink:label="lab_fac_AdvisoryAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Advisory Agreement, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_AdvisoryAgreementTerm" xlink:href="fac-20260630.xsd#fac_AdvisoryAgreementTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_AdvisoryAgreementTerm" xlink:to="lab_fac_AdvisoryAgreementTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_019fa592-a2be-7d0b-9da2-884dc2a5cf9e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Research and development, net (includes $10 and $140 for the three months ended June 30, 2026 and 2025, respectively; and $10 and $165 for the six months ended June 30, 2026 and 2025, respectively, of related party research and development reimbursement)</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_019fa590-c7ec-769a-aa01-ff8f46df386b_verboseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Research and development, net</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_019fca85-e29b-766d-be31-322bc32a8443_negatedLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Research and development expense</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_label_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Research and Development Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ResearchAndDevelopmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpense" xlink:to="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_019fafca-1a53-71ce-89c1-6eb21497f4f8_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share value</link:label>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Share Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputSharePriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputSharePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputSharePriceMember" xlink:to="lab_us-gaap_MeasurementInputSharePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare_019fa5ca-59dc-7f15-bb1e-2d8bbe2fea09_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, par value (in usd per share)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:to="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_RecapitalizationExchangeRatio_019faf0e-80f0-7b58-bcd2-0a1927f0e4d2_terseLabel_en-US" xlink:label="lab_fac_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion ratio</link:label>
    <link:label id="lab_fac_RecapitalizationExchangeRatio_label_en-US" xlink:label="lab_fac_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recapitalization Exchange Ratio</link:label>
    <link:label id="lab_fac_RecapitalizationExchangeRatio_documentation_en-US" xlink:label="lab_fac_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Recapitalization Exchange Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_RecapitalizationExchangeRatio" xlink:href="fac-20260630.xsd#fac_RecapitalizationExchangeRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_RecapitalizationExchangeRatio" xlink:to="lab_fac_RecapitalizationExchangeRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019fa60c-7e20-7ca0-a8dc-9ed6eb44f114_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_019fa5b4-f9a0-79b8-85f2-57ce97a97b14_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, after Accumulated Depreciation, Depletion, and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_019ff19d-dd8d-7e09-887f-3d8de31bb2ce_verboseLabel_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Redemption price (in usd per share)</link:label>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_019fca27-38e4-78a9-b002-fda84d496458_terseLabel_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Converted instrument, issue (in usd per share)</link:label>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_label_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesIssuedPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesIssuedPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesIssuedPricePerShare" xlink:to="lab_us-gaap_SharesIssuedPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_DebtConversionTermsTwoMember_019fca19-9a18-7d82-af36-2740f97456c1_terseLabel_en-US" xlink:label="lab_fac_DebtConversionTermsTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Conversion Terms Two</link:label>
    <link:label id="lab_fac_DebtConversionTermsTwoMember_label_en-US" xlink:label="lab_fac_DebtConversionTermsTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion Terms Two [Member]</link:label>
    <link:label id="lab_fac_DebtConversionTermsTwoMember_documentation_en-US" xlink:label="lab_fac_DebtConversionTermsTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Conversion Terms Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_DebtConversionTermsTwoMember" xlink:href="fac-20260630.xsd#fac_DebtConversionTermsTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_DebtConversionTermsTwoMember" xlink:to="lab_fac_DebtConversionTermsTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_MeasurementInputSPACExitScenarioMember_019fafe2-7b34-78be-9487-76a7caca2b12_terseLabel_en-US" xlink:label="lab_fac_MeasurementInputSPACExitScenarioMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SPAC Exit Scenario</link:label>
    <link:label id="lab_fac_MeasurementInputSPACExitScenarioMember_label_en-US" xlink:label="lab_fac_MeasurementInputSPACExitScenarioMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, SPAC Exit Scenario [Member]</link:label>
    <link:label id="lab_fac_MeasurementInputSPACExitScenarioMember_documentation_en-US" xlink:label="lab_fac_MeasurementInputSPACExitScenarioMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, SPAC Exit Scenario</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_MeasurementInputSPACExitScenarioMember" xlink:href="fac-20260630.xsd#fac_MeasurementInputSPACExitScenarioMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_MeasurementInputSPACExitScenarioMember" xlink:to="lab_fac_MeasurementInputSPACExitScenarioMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_019fa5eb-68d6-7ab7-8481-fc45568154a7_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Numerator:</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_019fd87e-bd22-7859-ba4d-48975e4ae4c6_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Series A Common Stock from stock option exercises</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Stock Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SponsorAndDirectorMembersMember_019fd88f-33e2-74b8-b68d-42115fff8e4b_terseLabel_en-US" xlink:label="lab_fac_SponsorAndDirectorMembersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sponsor and Director Co</link:label>
    <link:label id="lab_fac_SponsorAndDirectorMembersMember_label_en-US" xlink:label="lab_fac_SponsorAndDirectorMembersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sponsor And Director Members [Member]</link:label>
    <link:label id="lab_fac_SponsorAndDirectorMembersMember_documentation_en-US" xlink:label="lab_fac_SponsorAndDirectorMembersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sponsor And Director Members</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SponsorAndDirectorMembersMember" xlink:href="fac-20260630.xsd#fac_SponsorAndDirectorMembersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SponsorAndDirectorMembersMember" xlink:to="lab_fac_SponsorAndDirectorMembersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_019fd88f-33e2-78d0-8ba1-dc0ee409e7bc_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issued during period, acquisition (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1_019fca27-38e4-742d-aebc-715f4c63c1e5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Converted instrument, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1_label_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Converted Instrument, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtConversionConvertedInstrumentSharesIssued1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:to="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesA1RedeemableConvertiblePreferredStockMember_019fa5c6-0d49-7c20-8332-412ce5d61a94_terseLabel_en-US" xlink:label="lab_fac_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-1 redeemable convertible preferred stock</link:label>
    <link:label id="lab_fac_SeriesA1RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_fac_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-1 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_fac_SeriesA1RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_fac_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-1 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:href="fac-20260630.xsd#fac_SeriesA1RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:to="lab_fac_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019fca85-8858-7dfa-b790-4da7314e7a35_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019fca9e-3cdd-78f8-ae1b-e80b37797d28_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SubscriptionAgreementsMember_019fd890-a7bd-718a-ba4f-8e40230d6d85_terseLabel_en-US" xlink:label="lab_fac_SubscriptionAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subscription Agreements</link:label>
    <link:label id="lab_fac_SubscriptionAgreementsMember_label_en-US" xlink:label="lab_fac_SubscriptionAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subscription Agreements [Member]</link:label>
    <link:label id="lab_fac_SubscriptionAgreementsMember_documentation_en-US" xlink:label="lab_fac_SubscriptionAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subscription Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SubscriptionAgreementsMember" xlink:href="fac-20260630.xsd#fac_SubscriptionAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SubscriptionAgreementsMember" xlink:to="lab_fac_SubscriptionAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_019fd7e0-1261-7fa3-8a1a-0de1bbabeeb4_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019fab6e-9911-7f74-a38a-994f365ef1a0_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value outstanding</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019fab6f-54fc-7d44-9b10-2b5c29632ecf_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_NoteholderMember_019faf96-170e-7b15-a6ba-7e2a9cb407d7_terseLabel_en-US" xlink:label="lab_fac_NoteholderMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noteholder</link:label>
    <link:label id="lab_fac_NoteholderMember_label_en-US" xlink:label="lab_fac_NoteholderMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noteholder [Member]</link:label>
    <link:label id="lab_fac_NoteholderMember_documentation_en-US" xlink:label="lab_fac_NoteholderMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noteholder</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_NoteholderMember" xlink:href="fac-20260630.xsd#fac_NoteholderMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_NoteholderMember" xlink:to="lab_fac_NoteholderMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019fca86-6cb0-74b1-99a9-cc5ab1193a97_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Loss from operations</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019f9eb7-cb83-740e-9ead-a26f191e4b57_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_019fcfa3-39af-7e44-8641-3183f7ed5b37_verboseLabel_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Warrants outstanding</link:label>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WarrantsAndRightsOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsOutstanding" xlink:to="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_019fa590-474e-7d0c-ad10-a49319f60eb5_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_019fd890-a7bd-7e47-8670-5c9a3ad30797_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchased during period (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_019fed01-190a-791a-9d0b-502355e34e8f_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease agreement, total expected cash payments</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable_019fd288-9724-7985-984d-f1114b59453e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted, by Common Class, Including Two-Class Method [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted, by Common Class, Including Two-Class Method [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019f9eb7-cb82-7fdf-8344-52bdf465c7eb_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_TemporaryEquityConversionBasis_019fd7fe-b524-7130-89ce-9f52d15f48d9_terseLabel_en-US" xlink:label="lab_fac_TemporaryEquityConversionBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion basis</link:label>
    <link:label id="lab_fac_TemporaryEquityConversionBasis_label_en-US" xlink:label="lab_fac_TemporaryEquityConversionBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Conversion Basis</link:label>
    <link:label id="lab_fac_TemporaryEquityConversionBasis_documentation_en-US" xlink:label="lab_fac_TemporaryEquityConversionBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Conversion Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_TemporaryEquityConversionBasis" xlink:href="fac-20260630.xsd#fac_TemporaryEquityConversionBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_TemporaryEquityConversionBasis" xlink:to="lab_fac_TemporaryEquityConversionBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsCurrent_019fa5ad-5598-7569-aa28-5c7c3adda877_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred transaction costs</link:label>
    <link:label id="lab_us-gaap_DeferredCostsCurrent_label_en-US" xlink:label="lab_us-gaap_DeferredCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredCostsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsCurrent" xlink:to="lab_us-gaap_DeferredCostsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019fa5eb-68d6-7b48-a318-03310a4a487b_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_LegacyFactorialConvertibleNotesShareholdersMember_019fd890-a7bd-7fc4-a999-953ce3dfcc34_terseLabel_en-US" xlink:label="lab_fac_LegacyFactorialConvertibleNotesShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legacy Factorial Convertible Notes Shareholders</link:label>
    <link:label id="lab_fac_LegacyFactorialConvertibleNotesShareholdersMember_label_en-US" xlink:label="lab_fac_LegacyFactorialConvertibleNotesShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legacy Factorial Convertible Notes Shareholders [Member]</link:label>
    <link:label id="lab_fac_LegacyFactorialConvertibleNotesShareholdersMember_documentation_en-US" xlink:label="lab_fac_LegacyFactorialConvertibleNotesShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Legacy Factorial Convertible Notes Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_LegacyFactorialConvertibleNotesShareholdersMember" xlink:href="fac-20260630.xsd#fac_LegacyFactorialConvertibleNotesShareholdersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_LegacyFactorialConvertibleNotesShareholdersMember" xlink:to="lab_fac_LegacyFactorialConvertibleNotesShareholdersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019fa5a6-3a6f-7278-a93f-62bcc33fb978_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ReverseRecapitalizationDisclosureTextBlock_019faf03-e15a-7da8-afc6-1ff6a3873a64_terseLabel_en-US" xlink:label="lab_fac_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:label id="lab_fac_ReverseRecapitalizationDisclosureTextBlock_label_en-US" xlink:label="lab_fac_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization Disclosure [Text Block]</link:label>
    <link:label id="lab_fac_ReverseRecapitalizationDisclosureTextBlock_documentation_en-US" xlink:label="lab_fac_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ReverseRecapitalizationDisclosureTextBlock" xlink:href="fac-20260630.xsd#fac_ReverseRecapitalizationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ReverseRecapitalizationDisclosureTextBlock" xlink:to="lab_fac_ReverseRecapitalizationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019fce46-7c68-7a70-99f9-29689b5d56c5_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_StellantisMember_019fca9e-a651-777d-be90-a8f4b941ab0e_terseLabel_en-US" xlink:label="lab_fac_StellantisMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stellantis</link:label>
    <link:label id="lab_fac_StellantisMember_label_en-US" xlink:label="lab_fac_StellantisMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stellantis [Member]</link:label>
    <link:label id="lab_fac_StellantisMember_documentation_en-US" xlink:label="lab_fac_StellantisMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stellantis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_StellantisMember" xlink:href="fac-20260630.xsd#fac_StellantisMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_StellantisMember" xlink:to="lab_fac_StellantisMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_019fa590-474e-716b-a2ca-24f8a47610b6_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_019fb562-defc-7d7b-9b90-770f9e423ff4_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_StockConvertedReverseRecapitalization_019fd88f-33e2-7346-a962-e3c65cecc8cb_terseLabel_en-US" xlink:label="lab_fac_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Converted, reverse recapitalization (in shares)</link:label>
    <link:label id="lab_fac_StockConvertedReverseRecapitalization_label_en-US" xlink:label="lab_fac_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Converted, Reverse Recapitalization</link:label>
    <link:label id="lab_fac_StockConvertedReverseRecapitalization_documentation_en-US" xlink:label="lab_fac_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Converted, Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_StockConvertedReverseRecapitalization" xlink:href="fac-20260630.xsd#fac_StockConvertedReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_StockConvertedReverseRecapitalization" xlink:to="lab_fac_StockConvertedReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_WarrantsTextBlock_019fdc87-24d7-7263-8916-badf503af0cd_terseLabel_en-US" xlink:label="lab_fac_WarrantsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">WARRANTS</link:label>
    <link:label id="lab_fac_WarrantsTextBlock_label_en-US" xlink:label="lab_fac_WarrantsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants [Text Block]</link:label>
    <link:label id="lab_fac_WarrantsTextBlock_documentation_en-US" xlink:label="lab_fac_WarrantsTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_WarrantsTextBlock" xlink:href="fac-20260630.xsd#fac_WarrantsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_WarrantsTextBlock" xlink:to="lab_fac_WarrantsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassAMember_019fb53e-4952-7a06-a87e-fe2b8d378565_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Series A Common Stock, par value $0.00001 per share</link:label>
    <link:label id="lab_us-gaap_CommonClassAMember_019fa5da-c1f5-7527-afb9-833bb6efd8f6_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A Common stock</link:label>
    <link:label id="lab_us-gaap_CommonClassAMember_label_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class A [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassAMember" xlink:to="lab_us-gaap_CommonClassAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019f9eb7-cb83-715f-b3d7-3d1502903a6e_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019f9eb7-cb83-7b1a-81de-70c19e68d861_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019fcfcd-ed5b-77a8-a5a1-768b2522a777_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive loss</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_019f9ec2-034e-7c48-8b84-2910f1513eb8_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_GatemoreCapitalManagementMember_019ff119-2c5d-7192-8781-3fe0915b1190_terseLabel_en-US" xlink:label="lab_fac_GatemoreCapitalManagementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gatemore Capital Management</link:label>
    <link:label id="lab_fac_GatemoreCapitalManagementMember_label_en-US" xlink:label="lab_fac_GatemoreCapitalManagementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gatemore Capital Management [Member]</link:label>
    <link:label id="lab_fac_GatemoreCapitalManagementMember_documentation_en-US" xlink:label="lab_fac_GatemoreCapitalManagementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gatemore Capital Management</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_GatemoreCapitalManagementMember" xlink:href="fac-20260630.xsd#fac_GatemoreCapitalManagementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_GatemoreCapitalManagementMember" xlink:to="lab_fac_GatemoreCapitalManagementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_CommonStockAndPreferredStockSharesAuthorized_019fb562-defc-7919-99c8-2293e3863986_terseLabel_en-US" xlink:label="lab_fac_CommonStockAndPreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Authorized (in shares)</link:label>
    <link:label id="lab_fac_CommonStockAndPreferredStockSharesAuthorized_label_en-US" xlink:label="lab_fac_CommonStockAndPreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock And Preferred Stock, Shares Authorized</link:label>
    <link:label id="lab_fac_CommonStockAndPreferredStockSharesAuthorized_documentation_en-US" xlink:label="lab_fac_CommonStockAndPreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock And Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_CommonStockAndPreferredStockSharesAuthorized" xlink:href="fac-20260630.xsd#fac_CommonStockAndPreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_CommonStockAndPreferredStockSharesAuthorized" xlink:to="lab_fac_CommonStockAndPreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_019fab5a-72dd-7da3-8a6e-8ba8063c98e6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtConversionOriginalDebtAmount1_019fa648-4b67-7ed1-b729-73dc80681bb9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of convertible promissory notes and accrued interest into Series A Common Stock</link:label>
    <link:label id="lab_us-gaap_DebtConversionOriginalDebtAmount1_label_en-US" xlink:label="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Original Debt, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtConversionOriginalDebtAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtConversionOriginalDebtAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtConversionOriginalDebtAmount1" xlink:to="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_PIPESponsorInvestorMember_019fd88f-33e2-7ca9-87e6-6fb2ea3434e7_terseLabel_en-US" xlink:label="lab_fac_PIPESponsorInvestorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PIPE Sponsor Investor</link:label>
    <link:label id="lab_fac_PIPESponsorInvestorMember_label_en-US" xlink:label="lab_fac_PIPESponsorInvestorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PIPE Sponsor Investor [Member]</link:label>
    <link:label id="lab_fac_PIPESponsorInvestorMember_documentation_en-US" xlink:label="lab_fac_PIPESponsorInvestorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">PIPE Sponsor Investor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_PIPESponsorInvestorMember" xlink:href="fac-20260630.xsd#fac_PIPESponsorInvestorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_PIPESponsorInvestorMember" xlink:to="lab_fac_PIPESponsorInvestorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollaborativeArrangementAccountingPolicy_019faf19-d9fa-7e6a-83f2-0dcc9d5af46d_terseLabel_en-US" xlink:label="lab_us-gaap_CollaborativeArrangementAccountingPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaboration Arrangements and Partnership Agreements</link:label>
    <link:label id="lab_us-gaap_CollaborativeArrangementAccountingPolicy_label_en-US" xlink:label="lab_us-gaap_CollaborativeArrangementAccountingPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Accounting Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollaborativeArrangementAccountingPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CollaborativeArrangementAccountingPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollaborativeArrangementAccountingPolicy" xlink:to="lab_us-gaap_CollaborativeArrangementAccountingPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_019fa5a6-3a6f-7a57-99b4-7dadac33d067_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-current assets (related party)</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019f9eb7-a63b-76c8-953f-c918781c9cdd_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_019fab5a-72dd-7b2a-8723-0d73ed57b472_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_019f9ed9-873e-7737-be7d-4b5007cc9590_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_019f9ed9-e57a-78a9-92e3-316764a78ad0_totalLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaidInKindInterest_019fa616-02cf-7d2f-b39f-383b1999e298_terseLabel_en-US" xlink:label="lab_us-gaap_PaidInKindInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash interest</link:label>
    <link:label id="lab_us-gaap_PaidInKindInterest_label_en-US" xlink:label="lab_us-gaap_PaidInKindInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Paid-in-Kind Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaidInKindInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaidInKindInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaidInKindInterest" xlink:to="lab_us-gaap_PaidInKindInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019faf18-61c8-7615-95e4-88a7a1c086ca_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_019fce60-b385-7d1c-873d-ea5c467ae494_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInTemporaryEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_019fed01-190a-7f09-9663-9dd99ad68b52_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019f9eb7-cb83-7c70-b8b1-69c016c9f2f6_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion_019fab6e-9911-7f44-89a3-63aefb79e6d1_negatedTerseLabel_en-US" xlink:label="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Conversion to shares of Series A Common Stock</link:label>
    <link:label id="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion_label_en-US" xlink:label="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Conversion</link:label>
    <link:label id="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion_documentation_en-US" xlink:label="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Conversion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion" xlink:href="fac-20260630.xsd#fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion" xlink:to="lab_fac_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversion" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_019fa5ca-bd1d-722d-a3e3-ece775f532a5_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquitySharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:to="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019f9eb7-cb82-7237-9fb2-bdf4156fec80_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019f9eb7-cb82-78a9-aafc-9839e1b02a5b_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ReverseRecapitalizationMember_019fd890-a7bd-7e71-aba3-4cf2e1184cb5_terseLabel_en-US" xlink:label="lab_fac_ReverseRecapitalizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:label id="lab_fac_ReverseRecapitalizationMember_label_en-US" xlink:label="lab_fac_ReverseRecapitalizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization [Member]</link:label>
    <link:label id="lab_fac_ReverseRecapitalizationMember_documentation_en-US" xlink:label="lab_fac_ReverseRecapitalizationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ReverseRecapitalizationMember" xlink:href="fac-20260630.xsd#fac_ReverseRecapitalizationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ReverseRecapitalizationMember" xlink:to="lab_fac_ReverseRecapitalizationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019fd7a6-3dc1-76e8-9473-06505ad74eed_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Loss before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019fa5a6-3a6f-7a87-8a7d-7a5340208fb5_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 9)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_019fa5eb-68d6-78c2-a6c9-3f6a1d945f17_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_019f9ec2-034e-7d58-883d-a400bfa87a72_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, before Accumulated Depreciation, Depletion, and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentGross" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_019f9ec2-034e-7bb9-bde6-b069c85633e4_terseLabel_en-US" xlink:label="lab_us-gaap_MachineryAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Machinery and equipment</link:label>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_label_en-US" xlink:label="lab_us-gaap_MachineryAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Machinery and Equipment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MachineryAndEquipmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MachineryAndEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MachineryAndEquipmentMember" xlink:to="lab_us-gaap_MachineryAndEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_019f9ec2-034e-7e4b-943a-47eb2c257d3c_terseLabel_en-US" xlink:label="lab_us-gaap_FurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture and fixtures</link:label>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_label_en-US" xlink:label="lab_us-gaap_FurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture and Fixtures [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FurnitureAndFixturesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FurnitureAndFixturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FurnitureAndFixturesMember" xlink:to="lab_us-gaap_FurnitureAndFixturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_019faf8f-98c9-7116-9634-cc2bc47957a0_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019fa5a6-3a6f-7942-be61-e1c6a596df1b_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities, Redeemable Convertible Preferred Stock &amp; Stockholders&#8217; Equity (Deficit)</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_019fa5c2-4be5-7920-81a8-e0c88d4b5e1d_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total redeemable convertible preferred stock</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_019fce63-b86c-7c91-a927-e4ed450c691e_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_019fce63-d1c2-7051-9349-b7ec2bb613f8_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Carrying Amount, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesC2RedeemableConvertiblePreferredStockMember_019fa5c8-7886-7a9f-995f-d9f15e698db8_terseLabel_en-US" xlink:label="lab_fac_SeriesC2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series C-2 redeemable convertible preferred stock</link:label>
    <link:label id="lab_fac_SeriesC2RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_fac_SeriesC2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series C-2 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_fac_SeriesC2RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_fac_SeriesC2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series C-2 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesC2RedeemableConvertiblePreferredStockMember" xlink:href="fac-20260630.xsd#fac_SeriesC2RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesC2RedeemableConvertiblePreferredStockMember" xlink:to="lab_fac_SeriesC2RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_019fab49-ac5b-7ebd-a0b3-24563d809eb5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_019fcea5-3f27-7ae2-9158-ea124b1839dc_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:to="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019fab48-43e9-7c92-8c72-9221fd77b085_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FAIR VALUE MEASURES</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019fab59-ec1f-73cf-9137-697df67e2479_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_MeasurementInputFutureProjectedPricePerShareMember_019fdc94-268a-7cf5-9d53-773dbb37b00f_terseLabel_en-US" xlink:label="lab_fac_MeasurementInputFutureProjectedPricePerShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future projected price per share</link:label>
    <link:label id="lab_fac_MeasurementInputFutureProjectedPricePerShareMember_label_en-US" xlink:label="lab_fac_MeasurementInputFutureProjectedPricePerShareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Future Projected Price Per Share [Member]</link:label>
    <link:label id="lab_fac_MeasurementInputFutureProjectedPricePerShareMember_documentation_en-US" xlink:label="lab_fac_MeasurementInputFutureProjectedPricePerShareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Future Projected Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_MeasurementInputFutureProjectedPricePerShareMember" xlink:href="fac-20260630.xsd#fac_MeasurementInputFutureProjectedPricePerShareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_MeasurementInputFutureProjectedPricePerShareMember" xlink:to="lab_fac_MeasurementInputFutureProjectedPricePerShareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019fa60c-7e20-7dff-bc66-c7a684bc68cd_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger_019fca19-9a18-7a57-bc3f-8215c56adac3_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Threshold percentage of stock price trigger</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible, Threshold Percentage of Stock Price Trigger</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger" xlink:to="lab_us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_019fa617-850a-7ed3-813f-3ef7d949ccac_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_019f9ec2-034e-72b1-812d-2415d56da812_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasehold improvements</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasehold Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseholdImprovementsMember" xlink:to="lab_us-gaap_LeaseholdImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_019fa5cd-8fe4-7eae-a914-34d83d978d6d_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_019fcfdb-a089-7f89-9f2d-153d7ca363b6_verboseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Factorial Shares Issued</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquitySharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesIssued" xlink:to="lab_us-gaap_TemporaryEquitySharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_MeasurementInputDividendYieldMember_019fd7b6-8124-7c77-beff-fed702a1ef15_terseLabel_en-US" xlink:label="lab_fac_MeasurementInputDividendYieldMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend yield</link:label>
    <link:label id="lab_fac_MeasurementInputDividendYieldMember_label_en-US" xlink:label="lab_fac_MeasurementInputDividendYieldMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Dividend Yield [Member]</link:label>
    <link:label id="lab_fac_MeasurementInputDividendYieldMember_documentation_en-US" xlink:label="lab_fac_MeasurementInputDividendYieldMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Dividend Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_MeasurementInputDividendYieldMember" xlink:href="fac-20260630.xsd#fac_MeasurementInputDividendYieldMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_MeasurementInputDividendYieldMember" xlink:to="lab_fac_MeasurementInputDividendYieldMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization_019fce55-23a8-736f-b25a-a2127a2685bf_terseLabel_en-US" xlink:label="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock in connection with reverse recapitalization and PIPE Financing, net of issuance costs</link:label>
    <link:label id="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization_019fd8ad-8f33-7caa-888c-4b4cae058d01_verboseLabel_en-US" xlink:label="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization_label_en-US" xlink:label="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Reverse Recapitalization</link:label>
    <link:label id="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization_documentation_en-US" xlink:label="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:href="fac-20260630.xsd#fac_StockIssuedDuringPeriodValueReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:to="lab_fac_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_019f9ec2-034e-7c0c-8288-4641e7b55a6f_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019f9eb7-cb82-7664-852d-a6662e4071b5_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019fd7ee-938a-73c9-a1a7-bf824419a898_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_019fca27-38e4-765f-8ba8-18128d61d94a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_019fab6e-9911-728c-b065-1dc3df5b6e35_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember_019fab56-e57d-72ae-816f-55ab068cb292_terseLabel_en-US" xlink:label="lab_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series B-1 and Series D redeemable convertible preferred stock warrants</link:label>
    <link:label id="lab_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember_label_en-US" xlink:label="lab_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series B-1 And D Redeemable Convertible Preferred Stock Warrants [Member]</link:label>
    <link:label id="lab_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember_documentation_en-US" xlink:label="lab_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series B-1 And D Redeemable Convertible Preferred Stock Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember" xlink:href="fac-20260630.xsd#fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember" xlink:to="lab_fac_SeriesB1AndDRedeemableConvertiblePreferredStockWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesACommonStockPrivateWarrantsMember_019fb53e-53e1-7649-ae82-7924ff0d3111_verboseLabel_en-US" xlink:label="lab_fac_SeriesACommonStockPrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Warrants, each whole warrant exercisable for one share of Series A Common Stock at an exercise price of $11.50</link:label>
    <link:label id="lab_fac_SeriesACommonStockPrivateWarrantsMember_019fafaa-54f3-755a-a568-a26c995e8d3c_terseLabel_en-US" xlink:label="lab_fac_SeriesACommonStockPrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants for Series A</link:label>
    <link:label id="lab_fac_SeriesACommonStockPrivateWarrantsMember_label_en-US" xlink:label="lab_fac_SeriesACommonStockPrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A Common Stock Private Warrants [Member]</link:label>
    <link:label id="lab_fac_SeriesACommonStockPrivateWarrantsMember_documentation_en-US" xlink:label="lab_fac_SeriesACommonStockPrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A Common Stock Private Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesACommonStockPrivateWarrantsMember" xlink:href="fac-20260630.xsd#fac_SeriesACommonStockPrivateWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesACommonStockPrivateWarrantsMember" xlink:to="lab_fac_SeriesACommonStockPrivateWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019fa60c-7e20-76ba-86bb-2da087b2c809_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019fa60c-7e20-7278-98d8-ee8a9d9b7b99_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019fa60c-7e20-75bb-a95e-93f6a2aec8a3_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedProfessionalFeesCurrent_019f9ed9-873e-763d-8fbe-62dddf71eac4_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedProfessionalFeesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued legal and professional</link:label>
    <link:label id="lab_us-gaap_AccruedProfessionalFeesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedProfessionalFeesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Professional Fees, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedProfessionalFeesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedProfessionalFeesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedProfessionalFeesCurrent" xlink:to="lab_us-gaap_AccruedProfessionalFeesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_019faf8f-98c9-7dc2-a6c0-e14d3eb43df9_terseLabel_en-US" xlink:label="lab_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]</link:label>
    <link:label id="lab_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_label_en-US" xlink:label="lab_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems" xlink:to="lab_us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayable_019fa617-2e10-77b8-8df6-918bf9669529_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_019f9ed9-873e-7b6f-a221-ac7a4f364675_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued other</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019f9eb7-cb82-7681-a993-fd35fbed4896_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_019fce53-6fd3-7a24-ac0b-75fea7f6eec3_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of redeemable convertible preferred stock into Series A Common Stock (in shares)</link:label>
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    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeAxis"/>
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    <link:label id="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember_019fafca-bd04-724b-838a-15914fea07f0_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed risk-free interest rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Risk Free Interest Rate [Member]</link:label>
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    <link:label id="lab_us-gaap_AwardTypeAxis_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
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    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_019fa5af-7ad0-7ab7-b9c6-91559f5e0b7c_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
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    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
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    <link:label id="lab_fac_TemporaryEquityDisclosureTextBlock_019fb582-19dc-7c33-86c1-f669b45c5cf5_terseLabel_en-US" xlink:label="lab_fac_TemporaryEquityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">REDEEMABLE CONVERTIBLE PREFERRED STOCK</link:label>
    <link:label id="lab_fac_TemporaryEquityDisclosureTextBlock_label_en-US" xlink:label="lab_fac_TemporaryEquityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity Disclosure [Text Block]</link:label>
    <link:label id="lab_fac_TemporaryEquityDisclosureTextBlock_documentation_en-US" xlink:label="lab_fac_TemporaryEquityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_TemporaryEquityDisclosureTextBlock" xlink:href="fac-20260630.xsd#fac_TemporaryEquityDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_TemporaryEquityDisclosureTextBlock" xlink:to="lab_fac_TemporaryEquityDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ProceedsFromReverseRecapitalizationTransactionGross_019fd2aa-b05e-738c-9d7f-d6c9e5cbc841_terseLabel_en-US" xlink:label="lab_fac_ProceedsFromReverseRecapitalizationTransactionGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds received from reverse recapitalization, gross</link:label>
    <link:label id="lab_fac_ProceedsFromReverseRecapitalizationTransactionGross_label_en-US" xlink:label="lab_fac_ProceedsFromReverseRecapitalizationTransactionGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Reverse Recapitalization Transaction, Gross</link:label>
    <link:label id="lab_fac_ProceedsFromReverseRecapitalizationTransactionGross_documentation_en-US" xlink:label="lab_fac_ProceedsFromReverseRecapitalizationTransactionGross" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Reverse Recapitalization Transaction, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ProceedsFromReverseRecapitalizationTransactionGross" xlink:href="fac-20260630.xsd#fac_ProceedsFromReverseRecapitalizationTransactionGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ProceedsFromReverseRecapitalizationTransactionGross" xlink:to="lab_fac_ProceedsFromReverseRecapitalizationTransactionGross" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_019fafc8-9ac3-7575-a19c-495e12ef075d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_WarrantsAbstract_label_en-US" xlink:label="lab_fac_WarrantsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants [Abstract]</link:label>
    <link:label id="lab_fac_WarrantsAbstract_documentation_en-US" xlink:label="lab_fac_WarrantsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_WarrantsAbstract" xlink:href="fac-20260630.xsd#fac_WarrantsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_WarrantsAbstract" xlink:to="lab_fac_WarrantsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019fa5a6-3a6f-773e-aca4-47756f38651c_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities, Redeemable Convertible Preferred Stock &amp; Stockholders&#8217; Equity (Deficit)</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesNoncurrent_019fafa8-c671-7f4c-a133-51c8bdcd5e1f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:to="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ClearStreetLLCClearStreetMember_019fd7e0-1261-70e0-ade0-e2ac31545076_terseLabel_en-US" xlink:label="lab_fac_ClearStreetLLCClearStreetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Clear Street LLC (&#8220;Clear Street&#8221;)</link:label>
    <link:label id="lab_fac_ClearStreetLLCClearStreetMember_label_en-US" xlink:label="lab_fac_ClearStreetLLCClearStreetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Clear Street LLC (&#8220;Clear Street&#8221;) [Member]</link:label>
    <link:label id="lab_fac_ClearStreetLLCClearStreetMember_documentation_en-US" xlink:label="lab_fac_ClearStreetLLCClearStreetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Clear Street LLC (&#8220;Clear Street&#8221;)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ClearStreetLLCClearStreetMember" xlink:href="fac-20260630.xsd#fac_ClearStreetLLCClearStreetMember"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDilutedLineItems_019fd288-9724-76f1-b9bb-e7da195ca23f_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedLineItems_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDilutedLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDilutedLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDilutedLineItems" xlink:to="lab_us-gaap_EarningsPerShareDilutedLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_019fa5eb-68d6-7527-9a2d-b715570084ef_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options to purchase Series A Common Stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019fdc9c-f0d4-7f1d-9a34-cc7ea5ee81dc_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019fab6e-9911-7d17-b125-f012cbf36ffa_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_019fafc8-9ac3-7e64-9762-1dda9a7f66d3_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant liability, measurement input</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:to="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_SeriesC1RedeemableConvertiblePreferredStockMember_019fa5c8-363a-703a-9032-1e1d6b872013_terseLabel_en-US" xlink:label="lab_fac_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series C-1 redeemable convertible preferred stock</link:label>
    <link:label id="lab_fac_SeriesC1RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_fac_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series C-1 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_fac_SeriesC1RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_fac_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series C-1 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:href="fac-20260630.xsd#fac_SeriesC1RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:to="lab_fac_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019fa5a6-3a6f-72d7-bd60-e4a62bfdd540_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_019fca85-8858-770c-95ac-52aca784a71d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_DebtInstrumentConvertibleTermsOfConversionAxis_019fca19-9a18-7324-873f-8605ac41eda6_terseLabel_en-US" xlink:label="lab_fac_DebtInstrumentConvertibleTermsOfConversionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible Terms Of Conversion [Axis]</link:label>
    <link:label id="lab_fac_DebtInstrumentConvertibleTermsOfConversionAxis_label_en-US" xlink:label="lab_fac_DebtInstrumentConvertibleTermsOfConversionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible Terms Of Conversion [Axis]</link:label>
    <link:label id="lab_fac_DebtInstrumentConvertibleTermsOfConversionAxis_documentation_en-US" xlink:label="lab_fac_DebtInstrumentConvertibleTermsOfConversionAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible Terms Of Conversion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_DebtInstrumentConvertibleTermsOfConversionAxis" xlink:href="fac-20260630.xsd#fac_DebtInstrumentConvertibleTermsOfConversionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_DebtInstrumentConvertibleTermsOfConversionAxis" xlink:to="lab_fac_DebtInstrumentConvertibleTermsOfConversionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherOperatingIncomeExpenseNet_019fca85-8858-72ed-afa9-0b1fe4d6f142_terseLabel_en-US" xlink:label="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other operating expense</link:label>
    <link:label id="lab_us-gaap_OtherOperatingIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Operating Income (Expense), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherOperatingIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherOperatingIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherOperatingIncomeExpenseNet" xlink:to="lab_us-gaap_OtherOperatingIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_PIPEInstitutionalInvestorMember_019fd88f-33e2-7e24-8209-b240b56d3454_terseLabel_en-US" xlink:label="lab_fac_PIPEInstitutionalInvestorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PIPE Institutional Investor</link:label>
    <link:label id="lab_fac_PIPEInstitutionalInvestorMember_label_en-US" xlink:label="lab_fac_PIPEInstitutionalInvestorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PIPE Institutional Investor [Member]</link:label>
    <link:label id="lab_fac_PIPEInstitutionalInvestorMember_documentation_en-US" xlink:label="lab_fac_PIPEInstitutionalInvestorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">PIPE Institutional Investor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_PIPEInstitutionalInvestorMember" xlink:href="fac-20260630.xsd#fac_PIPEInstitutionalInvestorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_PIPEInstitutionalInvestorMember" xlink:to="lab_fac_PIPEInstitutionalInvestorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_019f9ec2-034e-7a16-8238-29e49a9ee473_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_019fab6e-9911-78fa-a048-bbcdf17bf216_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_019fd890-a7bd-7fd6-9fe3-dbdb4bcc8d15_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issued and sold (in usd per share)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_label_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockPricePerShare" xlink:to="lab_us-gaap_SaleOfStockPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_019fce53-6fd3-7f21-b270-41a25cc66dab_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of redeemable convertible preferred stock into Series A Common Stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_019fa5a6-3a6f-7cf5-9908-b381a83ccee8_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_019f9ec2-034e-7b12-8dbb-53d129113666_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentMeasurementInput_019fafe2-e1ca-7b7c-b61d-eb0bff1d1c61_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible promissory notes, measurement input</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentMeasurementInput" xlink:to="lab_us-gaap_DebtInstrumentMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_019fa5a6-3a6f-7062-9568-e6e1fb0b719e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, $0.00001 pare value, 100,000,000 authorized as of June 30, 2026. No shares were authorized as of December 31, 2025.</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_019fa5c6-0d49-7f6a-acc5-e2358fce86f3_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019fa60c-7e20-7ae5-bdef-9ea5d4193c3a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ReportableSegmentMember_019fdc9d-2a11-7a85-875a-36ed791d73ff_terseLabel_en-US" xlink:label="lab_fac_ReportableSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reportable Segment</link:label>
    <link:label id="lab_fac_ReportableSegmentMember_label_en-US" xlink:label="lab_fac_ReportableSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reportable Segment [Member]</link:label>
    <link:label id="lab_fac_ReportableSegmentMember_documentation_en-US" xlink:label="lab_fac_ReportableSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reportable Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ReportableSegmentMember" xlink:href="fac-20260630.xsd#fac_ReportableSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ReportableSegmentMember" xlink:to="lab_fac_ReportableSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019fab5a-e8ae-7288-b1d4-b79c98d9b02a_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ReimbursementIncome_019fca85-8858-7cef-a0ef-517190baae40_terseLabel_en-US" xlink:label="lab_fac_ReimbursementIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reimbursement from JDAs and others</link:label>
    <link:label id="lab_fac_ReimbursementIncome_label_en-US" xlink:label="lab_fac_ReimbursementIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reimbursement Income</link:label>
    <link:label id="lab_fac_ReimbursementIncome_documentation_en-US" xlink:label="lab_fac_ReimbursementIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reimbursement Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ReimbursementIncome" xlink:href="fac-20260630.xsd#fac_ReimbursementIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ReimbursementIncome" xlink:to="lab_fac_ReimbursementIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_019fa5a6-3a6f-7a0d-90ab-5dd3af165cc2_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable (includes $2 and $190 as related party, as of June&#160;30, 2026, and December&#160;31, 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_019fa5e6-5c90-77d9-a1d4-198058bf7206_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableCurrent" xlink:to="lab_us-gaap_AccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019fab59-ec1f-773a-9f73-4542dc9ff623_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019fb57c-8709-7ab5-bf79-35bae99818e3_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_DebtConversionTermsOneMember_019fca19-9a18-79c7-bab9-9f6a2c74a5df_terseLabel_en-US" xlink:label="lab_fac_DebtConversionTermsOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Conversion Terms One</link:label>
    <link:label id="lab_fac_DebtConversionTermsOneMember_label_en-US" xlink:label="lab_fac_DebtConversionTermsOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion Terms One [Member]</link:label>
    <link:label id="lab_fac_DebtConversionTermsOneMember_documentation_en-US" xlink:label="lab_fac_DebtConversionTermsOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Conversion Terms One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_DebtConversionTermsOneMember" xlink:href="fac-20260630.xsd#fac_DebtConversionTermsOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_DebtConversionTermsOneMember" xlink:to="lab_fac_DebtConversionTermsOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019fce46-7c68-7fbf-9145-b3ef9a5eb38b_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-In Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019f9eb7-cb83-7b3a-bf8a-be2a187b9374_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable_019fd7e0-1261-7692-8521-1a667e14b586_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:to="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionPeriod_019fcfa1-30c0-7cbc-b2cf-ec8af0d25dbe_terseLabel_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption period</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionPeriod_label_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption Period</link:label>
    <link:label id="lab_fac_ClassOfWarrantOrRightRedemptionPeriod_documentation_en-US" xlink:label="lab_fac_ClassOfWarrantOrRightRedemptionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ClassOfWarrantOrRightRedemptionPeriod" xlink:href="fac-20260630.xsd#fac_ClassOfWarrantOrRightRedemptionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ClassOfWarrantOrRightRedemptionPeriod" xlink:to="lab_fac_ClassOfWarrantOrRightRedemptionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementAxis_019fce46-7c68-70f2-9794-a196ebe1cca4_terseLabel_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:label id="lab_srt_RestatementAxis_label_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementAxis" xlink:to="lab_srt_RestatementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ScheduleOfReverseRecapitalizationTable_019fd88d-b3cc-768b-8173-2556639f4ca9_terseLabel_en-US" xlink:label="lab_fac_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Of Reverse Recapitalization [Table]</link:label>
    <link:label id="lab_fac_ScheduleOfReverseRecapitalizationTable_label_en-US" xlink:label="lab_fac_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Reverse Recapitalization [Table]</link:label>
    <link:label id="lab_fac_ScheduleOfReverseRecapitalizationTable_documentation_en-US" xlink:label="lab_fac_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Reverse Recapitalization [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ScheduleOfReverseRecapitalizationTable" xlink:href="fac-20260630.xsd#fac_ScheduleOfReverseRecapitalizationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ScheduleOfReverseRecapitalizationTable" xlink:to="lab_fac_ScheduleOfReverseRecapitalizationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019fa5a6-3a6f-77c7-b7eb-a337992d7ed4_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019fa60c-7e20-7b0c-a858-6287836108ab_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_019fafc3-e790-7ea4-8ab3-3789201a56d3_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected life</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Term [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputExpectedTermMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:to="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_ScheduleOfReverseRecapitalizationTableTextBlock_019faf0f-65cd-7a7b-946e-2ee6ebae8975_terseLabel_en-US" xlink:label="lab_fac_ScheduleOfReverseRecapitalizationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule Of Reverse Recapitalization</link:label>
    <link:label id="lab_fac_ScheduleOfReverseRecapitalizationTableTextBlock_label_en-US" xlink:label="lab_fac_ScheduleOfReverseRecapitalizationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Reverse Recapitalization [Table Text Block]</link:label>
    <link:label id="lab_fac_ScheduleOfReverseRecapitalizationTableTextBlock_documentation_en-US" xlink:label="lab_fac_ScheduleOfReverseRecapitalizationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_ScheduleOfReverseRecapitalizationTableTextBlock" xlink:href="fac-20260630.xsd#fac_ScheduleOfReverseRecapitalizationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_ScheduleOfReverseRecapitalizationTableTextBlock" xlink:to="lab_fac_ScheduleOfReverseRecapitalizationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_TemporaryEquitySharesConversionOfConvertibleSecurities_019fce53-0b8f-712f-81ce-915260b44fb0_negatedTerseLabel_en-US" xlink:label="lab_fac_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Conversion of redeemable convertible preferred stock and treasury stock into Series A common stock (in shares)</link:label>
    <link:label id="lab_fac_TemporaryEquitySharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_fac_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Conversion of Convertible Securities</link:label>
    <link:label id="lab_fac_TemporaryEquitySharesConversionOfConvertibleSecurities_documentation_en-US" xlink:label="lab_fac_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:href="fac-20260630.xsd#fac_TemporaryEquitySharesConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:to="lab_fac_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_019fa613-938e-7752-8933-622c50dd89d9_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019fb562-defc-7808-8f6d-5b47322120c5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_019fa5a6-3a6f-7222-891e-452161aca4a1_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets:</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019fafb2-64b4-74b5-aa80-b6dd12bde46a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019f9eb7-cb82-79b8-8a09-5a282e242460_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_JosephTaylorMember_019fcaa5-28dd-783d-ae6f-64abeec07f9d_terseLabel_en-US" xlink:label="lab_fac_JosephTaylorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Joseph Taylor</link:label>
    <link:label id="lab_fac_JosephTaylorMember_label_en-US" xlink:label="lab_fac_JosephTaylorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joseph Taylor [Member]</link:label>
    <link:label id="lab_fac_JosephTaylorMember_documentation_en-US" xlink:label="lab_fac_JosephTaylorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Joseph Taylor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_JosephTaylorMember" xlink:href="fac-20260630.xsd#fac_JosephTaylorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_JosephTaylorMember" xlink:to="lab_fac_JosephTaylorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019fd799-d901-7c29-aa9f-219b46aa185b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019fa60c-7e20-7128-848e-742d4c064b0f_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Noncash Item [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_019fca62-c918-7fd5-a975-5323b10c27a4_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityByClassOfStockTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityByClassOfStockTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityByClassOfStockTable" xlink:to="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019faf19-43d5-7465-b542-b6cb975d6c75_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019fa60c-7e20-7378-8472-596021f0a52b_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net change in cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts_019faf0c-8963-722a-b25d-3b23c25c4fc9_terseLabel_en-US" xlink:label="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction costs</link:label>
    <link:label id="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts_019fd2ac-3e6f-7045-9b1f-9b83d1114aee_verboseLabel_en-US" xlink:label="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Payments of transaction expenses</link:label>
    <link:label id="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts_label_en-US" xlink:label="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Reverse Recapitalization Transaction Costs</link:label>
    <link:label id="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts_documentation_en-US" xlink:label="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments of Reverse Recapitalization Transaction Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fac_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:href="fac-20260630.xsd#fac_PaymentsOfReverseRecapitalizationTransactionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fac_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:to="lab_fac_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019fca86-ab84-769d-b9e5-d0ea7ad0397a_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019fa5f2-7072-7fe2-acde-939b516ca093_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019fb577-faf6-7714-b307-4869d0b23dd8_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOtherTypesMember_019f9ec2-034e-7be6-a643-766399b6731b_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOtherTypesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advances on purchases of property and equipment</link:label>
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    <link:label id="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumAggregatePerformancePayments_019faf96-170e-7915-9bcb-b12bbeb6c6b7_terseLabel_en-US" xlink:label="lab_fac_CollaborativeArrangementRightsAndObligationsMaximumAggregatePerformancePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consideration for performance</link:label>
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    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized_019fa615-bb2b-7998-a086-5fe85e2551f7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized foreign exchange loss (gain)</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyTransactionGainLossUnrealized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss), Foreign Currency Transaction, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyTransactionGainLossUnrealized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossUnrealized"/>
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    <link:label id="lab_us-gaap_LossContingencyDamagesSoughtValue_label_en-US" xlink:label="lab_us-gaap_LossContingencyDamagesSoughtValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Damages Sought, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyDamagesSoughtValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyDamagesSoughtValue"/>
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    <link:label id="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1_019fed0c-e235-73a2-85b5-a22a2039361d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of convertible promissory notes</link:label>
    <link:label id="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1_019fed0c-20c0-7021-b2de-0e24ad67a2a3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of convertible promissory notes</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueOptionChangesInFairValueGainLoss1"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract_019fd26d-de3b-7151-b765-e258258bf00e_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Numerator:</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted [Abstract]</link:label>
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