Let \triangle A B C be a triangle with A B=4, B C=6, and C A=5. Let the angle bisector of \angle B A C intersect B C at the point D and the circumcircle of \triangle A B C again at the point M \neq A. The perpendicular bisector of segment D M intersects the circle centered at M passing through B at two points, X and Y. Compute A X \cdot A Y.