CWMO 2019 Problem 5

In acute-angled triangle $ABC,$ $AB>AC.$ Let $O,H$ be the circumcenter and orthocenter of $\triangle ABC,$ respectively. The line passing through $H$ and parallel to $AB$ intersects line $AC$ at $M,$ and the line passing through $H$ and parallel to $AC$ intersects line $AB$ at $N.$ $L$ is the reflection of the point $H$ in $MN.$ Line $OL$ and $AH$ intersect at $K.$ Prove that $K,M,L,N$ are concyclic.