In quadrilateral $ABCD$, where $AC = BD$ and $\angle B = 60^\circ$, denote by $M$ and $N$ the midpoints of $\overline{AB}$ and $\overline{CD}$, respectively. Given that $MN = 12$ and the area of quadrilateral $ABCD$ is 420, compute $AC$.

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