Given a square $ABCD$ with side length $10$. On sides $BC$ and $AD$ of this square, points $E$ and $F$ are selected such that they form a rectangle $ABEF$. Rectangle $KLMN$ is positioned such that its vertices $K, L, M$, and $N$ lie on segments $CD, DF, FE$, and $EC$, respectively. It is given that rectangles $ABEF$ and $KLMN$ are congruent with $AB = MN$. Find the length of segment $AL$.

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