SHARYGIN 2020 Problem 2

Let $ABCD$ be a cyclic quadrilateral. A circle passing through $A$ and $B$ meets $AC$ and $BD$ at points $E$ and $F$ respectively. The lines $AF$ and $BC$ meet at point $P$ , and the lines $BE$ and $AD$ meet at point $Q$ . Prove that $PQ$ is parallel to $CD$ .