In a rectangle $ABCD$, let $E$ be the midpoint of $AB$, and $F$ be a point on $AC$ such that $BF$ is perpendicular to $AC$, and $FE$ is perpendicular to $BD$. Suppose $BC = 8\sqrt{3}$. Find $AB$.

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