DE-BUNDESWETTBEWERB 2024 Problem 3

Let $ABCD$ be a parallelogram whose diagonals intersect in $M$ . Suppose that the circumcircle of $ABM$ intersects the segment $AD$ in a point $E \ne A$ and that the circumcircle of $EMD$ intersects the segment $BE$ in a point $F \ne E$ . Show that $\angle ACB=\angle DCF$ .