Given a square $ABCD$. Let $P \in AB$, $Q \in BC$, $R \in CD$, $S \in DA$ such that $PR \parallel BC$ and $SQ \parallel AB$. Let $Z = PR \cap SQ$. If $BP = 7$, $BQ = 6$, and $DZ = 5$, find the side length of the square.

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