BALKAN-SL 2021 G6

Let $A B C$ be an acute triangle such that $A B<A C$. Let $\omega$ be the circumcircle of $A B C$ and assume that the tangent to $\omega$ at $A$ intersects the line $B C$ at $D$. Let $\Omega$ be the circle with center $D$ and radius $A D$. Denote by $E$ the second intersection point of $\omega$ and $\Omega$. Let $M$ be the midpoint of $B C$. If the line $B E$ meets $\Omega$ again at $X$, and the line $C X$ meets $\Omega$ for the second time at $Y$, show that $A, Y$ and $M$ are collinear.