In $\triangle ABC$, $AB=AC=28$ and $BC=20$. Points $D, E,$ and $F$ are on sides $\overline{AB}$, $\overline{BC}$, and $\overline{AC}$, respectively, such that $\overline{DE}$ and $\overline{EF}$ are parallel to $\overline{AC}$ and $\overline{AB}$, respectively. Find the perimeter of parallelogram $ADEF$.

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