HMMT November 2023 U5

Let $A B C D E$ be a convex pentagon such that

$$\begin{aligned} & A B+B C+C D+D E+E A=64 \text { and } \\ & A C+C E+E B+B D+D A=72 . \end{aligned}$$

Compute the perimeter of the convex pentagon whose vertices are the midpoints of the sides of $A B C D E$.