Right triangle $\triangle ABC$ with a right angle at $A$ has $AB = 20$ and $AC = 15$. Point $D$ is on $AB$ with $BD = 2$. Points $E$ and $F$ are placed on ray $CA$ and ray $CB$, respectively, such that $CD$ is a median of $\triangle CEF$. Find the area of $\triangle CEF$.

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