CZ-SK-MO 2023 Problem 5

In triangle $ABC$ let $N, M, P$ be the midpoints of the sides $BC, CA, AB$ and $G$ be the centroid of this triangle. Let the circle circumscribed to $BGP$ intersect the line $MP$ in point $K$ , $P \neq K$ , and the circle circumscribed to $CGN$ intersect the line $MN$ in point $L$ , $N \neq L$ . Prove that $\angle BAK = \angle CAL$ .