RU-ALLRUSSIAN 2021 Problem 108

Given is a cyclic pentagon $ABCDE$ , inscribed in a circle $k$ . The line $CD$ intersects $AB$ and $AE$ in $X$ and $Y$ respectively. Segments $EX$ and $BY$ intersect again at $P$ , and they intersect $k$ in $Q$ and $R$ , respectively. Point $A'$ is reflection of $A$ across $CD$ . The circles $(PQR)$ and $(A'XY)$ intersect at $M$ and $N$ . Prove that $CM$ and $DN$ intersect on $(PQR)$ .