AMC 10 2022a Problem 5

Square $ABCD$ has side length $1$. Points $P$, $Q$, $R$, and $S$ each lie on a side of $ABCD$ such that $APQCRS$ is an equilateral convex hexagon with side length $s$. What is $s$? $\textbf{(A) } \frac{\sqrt{2}}{3} \textbf{(B) } \frac{1}{2} \textbf{(C) } 2 - \sqrt{2} \textbf{(D) } 1 - \frac{\sqrt{2}}{4} \textbf{(E) } \frac{2}{3}$