Let ABCD be a square with side length 8. Let M be the midpoint of BC and let \omega be the circle passing through M, A, and D. Let O be the center of \omega, X be the intersection point (besides A) of \omega with AB, and Y be the intersection point of OX and AM. If the length of OY can be written in simplest form as \frac{m}{n}, compute m + n.