IMO 2025 — Complete Shortlist Question 22

Let $ABC$ be a triangle with $\angle B \gt \angle A \gt \angle C$. Let $\Omega$ be the circumcircle of triangle $ABC$. The lines tangent to $\Omega$ at points $B$ and $C$ intersect at $P$. Lines $BP$ and $AC$ intersect at $E$. Lines $CP$ and $AB$ intersect at $F$. Let $D$ be the reflection of point $A$ in line $EF$. The circumcircles of triangles $DEB$ and $DFC$ intersect again at $Q \neq D$. Lines $DP$ and $BC$ intersect at $Z$.

Prove that points A, Z and Q are collinear.