OSN 2020 Problem 6

Given a cyclic quadrilateral $ABCD$ . Let $X$ be a point on segment $BC$ ( $X \not= BC$ ) such that line $AX$ is perpendicular to the angle bisector of $\angle CBD$ , and $Y$ be a point on segment $AD$ ( $Y \not= D)$ such that $BY$ is perpendicular to the angle bisector of $\angle CAD$ . Prove that $XY$ is parallel to $CD$ .