Let $ABCD$ be a convex quadrilateral with $AC = 7$ and $BD = 17$. Let $M$, $P$, $N$, $Q$ be the midpoints of sides $AB$, $BC$, $CD$, and $DA$, respectively. Compute $MN^2 + PQ^2$.

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