CAPS 2019 Problem 1

Let $\omega$ be a circle. Points $A,B,C,X,D,Y$ lie on $\omega$ in this order such that $BD$ is its diameter and $DX=DY=DP$ , where $P$ is the intersection of $AC$ and $BD$ . Denote by $E,F$ the intersections of line $XP$ with lines $AB,BC$ , respectively. Prove that points $B,E,F,Y$ lie on a single circle.