# Origami Probability

A square sheet of paper has its center marked with point $O$. A random point is uniformly chosen on the square paper, and this point is labeled $P$. The paper is then folded so that point $P$ coincides with point $O$. Let the probability that a pentagon is formed after the fold be $N$. Find the value of $\lfloor 1000N \rfloor$.

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