AMC 12 2025b Problem 4

The value of the two-digit number $\underline{a}\;\underline{b}$ in base seven equals the value of the two-digit number $\underline{b}\;\underline{a}$ in base nine. What is $a+b$?

$\textbf{(A) } 7 \textbf{(B) } 9 \textbf{(C) } 10 \textbf{(D) } 11 \textbf{(E) } 14$