IZhO 2022 Problem 3

In parallelogram $ABCD$ with acute angle $A$ a point $N$ is chosen on the segment $AD$ , and a point $M$ on the segment $CN$ so that $AB = BM = CM$ . Point $K$ is the reflection of $N$ in line $MD$ . The line $MK$ meets the segment $AD$ at point $L$ . Let $P$ be the common point of the circumcircles of $AMD$ and $CNK$ such that $A$ and $P$ share the same side of the line $MK$ . Prove that $\angle CPM = \angle DPL$ .