Let $ABCD$ be a quadrilateral such that $\angle ABC = \angle  CDA = 90^o$, and $BC = 7$. Let $E$ and $F$ be on $BD$ such that $AE$ and $CF$ are perpendicular to BD. Suppose that $BE = 3$. Determine the product of the smallest and largest possible lengths of $DF$.

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