HMMT 2014 G8

Let $A B C$ be a triangle with sides $A B=6, B C=10$, and $C A=8$. Let $M$ and $N$ be the midpoints of $B A$ and $B C$, respectively. Choose the point $Y$ on ray $C M$ so that the circumcircle of triangle $A M Y$ is tangent to $A N$. Find the area of triangle $N A Y$.