MathNet 2023-part-03 — 191 problems (EN–VI) Question 1

Let $ABCD$ be a cyclic quadrilateral with $\angle BAD \lt \angle ADC$. Let $M$ be the midpoint of the arc $CD$ not containing $A$. Suppose there is a point $P$ inside $ABCD$ such that $\angle ADB = \angle CPD$ and $\angle ADP = \angle PCB$.
Prove that lines $AD$, $PM$, $BC$ are concurrent.