APMO 2024 - Asian Pacific Mathematics Olympiad Question 1

Let $ABC$ be an acute triangle. Let $D$ be a point on side $AB$ and $E$ a point on side $AC$ such that $BC\parallel DE$. Let $X$ be an interior point of $BCED$. Suppose rays $DX$ and $EX$ meet side $BC$ at points $P$ and $Q$, respectively, such that both $P,Q$ lie between $B,C$. Suppose the circumcircles of triangles $BQX$ and $CPX$ intersect at $Y\ne X$. Prove that $A,X,Y$ are collinear.

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