Perform the indicated operation. \[ 13 \frac{2}{5}+23 \frac{2}{3} \] \[ 13 \frac{2}{5}+23 \frac{2}{3}= \] (Simplify your answer.)

Step 1 ：Convert each mixed number to an improper fraction. The first number, \(13 \frac{2}{5}\), becomes \(\frac{67}{5}\) and the second number, \(23 \frac{2}{3}\), becomes \(\frac{71}{3}\).

Step 2 ：Add the two fractions together. \(\frac{67}{5} + \frac{71}{3} = \frac{556}{15}\).

Step 3 ：Simplify the result. \(\frac{556}{15}\) simplifies to \(37 \frac{1}{15}\).

Step 4 ：Convert the result back to a mixed number. The final answer is \(\boxed{37 \frac{1}{15}}\).