Carlen is a cash basis taxpayer. In $2023,$ Carlen paid state income taxes of $$12,000.$ In early $2024,$ Carlen filed the $2023$ state income tax return and received a $$1,200$ refund. Which of the following statements is true?

a$.$ Carlen does not have to worry about the $$1,200$ refund because refunds are never included in the next year's income under any circumstances. They are exempt from Federal tax.

b$.$ If Carlen took the standard deduction on the $2023$ Federal income tax return, Carlen does not have to include the $$1,200$ in the $2024$ Federal gross income.

c$.$ If Carlen took the standard deduction on the $2023$ Federal income tax return, Carlen must include the $$1,200$ in the $2024$ Federal gross income.

d$.$ If Carlen itemized deductions in $2023$ on the Federal income tax return and the itemized deductions exceeded the standard deduction by at least $$1,200,$ Carlen must include the $$1,200$ in the $2024$ Federal gross income.

e$.$ If Carlen itemized deductions in $2023,$ Carlen must amend the $2023$ Federal income tax return to reduce the itemized deductions.