HMMT November 2015 H1

Consider a $1 \times 1$ grid of squares. Let $A, B, C, D$ be the vertices of this square, and let $E$ be the midpoint of segment $C D$. Furthermore, let $F$ be the point on segment $B C$ satisfying $B F=2 C F$, and let $P$ be the intersection of lines $A F$ and $B E$. Find $\frac{A P}{P F}$.