SMO 2023 Junior Round 2 Question 1

In a convex quadrilateral $ABCD$, the diagonals intersect at $O$, $M$ and $N$ are points on the segments $OA$ and $OD$ respectively. Suppose $MN$ is parallel to $AD$ and $NC$ is parallel to $AB$. Prove that $\angle ABM=\angle NCD$.