In $2023,$ Aurora received a $$32,100$ bonus computed as a percentage of profits. In $2024,$ Aurora's employer determined that the $2023$ profits had been incorrectly computed, and Aurora had to refund the $$9,630$ in $2024.$ Assume that Aurora was in the $35\%$ tax bracket in $2023$ but in the $12\%$ bracket in $2024.$

If required, round your final answers to the nearest dollar.

a$.$ In $2023,$ how much is Aurora required to include in gross income?

$fill in the blank $1$

b$.$ In $2024,$ what is the amount of the deduction Aurora can claim?

$fill in the blank $2$

What is the reduction in taxes for $2024$ as a result of the deduction?

$fill in the blank $3$