Let $ABCD$ be a parallelogram with $\angle ABC=120^\circ$, $AB=16$, and $BC=10$. Extend $\overline{CD}$ through $D$ to $E$ so that $DE=4$. If $\overline{BE}$ intersects $\overline{AD}$ at $F$, then find the length of $FD$.

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