CN-SMO 2020 Problem 6

In a quadrilateral $ABCD$ , $\angle ABC=\angle ADC <90^{\circ}$ . The circle with diameter $AC$ intersects $BC$ and $CD$ again at $E,F$ , respectively. $M$ is the midpoint of $BD$ , and $AN \perp BD$ at $N$ . Prove that $M,N,E,F$ is concyclic.