The triangle $ABC$ has side lengths $AB = 39$, $BC = 57$, and $CA = 70$. The median $\overline{AD}$ is divided into three congruent segments by points $E$ and $F$. Lines $BE$ and $BF$ intersect side $\overline{AC}$ at points $G$ and $H$, respectively. Find the distance from $G$ to $H$.

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