Dale and Mary, filing Married Filing Jointly, have two children: Robert, age $15,$ and Marcia, age $19.$ They also support Mary's father, age $59,$ who lives separately, as a dependent. For the $2023$ tax year, their Modified Adjusted Gross Income $($MAGI$)$ is $$40,000,$ and their income tax liability before credits is $$1,993.$ Additionally, they are eligible for an Earned Income Credit $($EIC$)$ of $$2,715$ and have calculated an Additional Child Tax Credit $($ACTC$)$ amount of $$507.$ Considering the maximum Child Tax Credit used to offset their tax liability brings their total tax to zero. What is the refundable portion of the Child Tax Credit they can expect on Form $1040$ for tax year $2023?$

a$)$ $$3,200$

b$)$ $$1,600$

c$)$ $$507$

d$)$ $$0$