AMC 12 2022a Problem 1

What is the value of $$3+\frac{1}{3+\frac{1}{3+\frac13}}?$$

\textbf{(A)}\ \frac{31}{10} \textbf{(B)}\ \frac{49}{15} \textbf{(C)}\ \frac{33}{10} \textbf{(D)}\ \frac{109}{33} \textbf{(E)}\ \frac{15}{4}