OIM 2019 Problem 3

Let $\Gamma$ be the circumcircle of triangle $ABC$ . The line parallel to $AC$ passing through $B$ meets $\Gamma$ at $D$ ( $D\neq B$ ), and the line parallel to $AB$ passing through $C$ intersects $\Gamma$ to $E$ ( $E\neq C$ ). Lines $AB$ and $CD$ meet at $P$ , and lines $AC$ and $BE$ meet at $Q$ . Let $M$ be the midpoint of $DE$ . Line $AM$ meets $\Gamma$ at $Y$ ( $Y\neq A$ ) and line $PQ$ at $J$ . Line $PQ$ intersects the circumcircle of triangle $BCJ$ at $Z$ ( $Z\neq J$ ). If lines $BQ$ and $CP$ meet each other at $X$ , show that $X$ lies on the line $YZ$ .