ISL 2023 G3

Let $A B C D$ be a cyclic quadrilateral with $\angle B A D<\angle A D C$. Let $M$ be the midpoint of the arc $C D$ not containing $A$. Suppose there is a point $P$ inside $A B C D$ such that $\angle A D B=$ $\angle C P D$ and $\angle A D P=\angle P C B$. Prove that lines $A D, P M, B C$ are concurrent.