Triangle $ABC$ is equilateral. Points $D$ and $E$ are the midpoints of segments $BC$ and $AC$, respectively. $F$ is the point on segment $AB$ such that $2BF = AF$. Let $P$ denote the intersection of $AD$ and $EF$. The value of $\frac{EP}{PF}$ can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Let's think step by step and output the final answer within \boxed{}.
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