The midpoints of the sides $BC, CA$, and $AB$ of triangle $ABC$ are $D, E$, and $F$, respectively. The reflections of centroid $M$ of $ABC$ around points $D, E$, and $F$ are $X, Y$, and $Z$, respectively. Segments $XZ$ and $YZ$ intersect the side $AB$ in points $K$ and $L$, respectively. Prove that $AL = BK$.