VTMO 2026 - Grade 8 - Final - SET 4 - Self-study Question 1

In parallelogram $ABCD$, $AB>AD$. Point $E$ lies on side $AB$ with $AE=AD$. Let $F=DE\cap AC$. Take $K$ on segment $EF$, and let $M=AK\cap BC$, $N=CK\cap AB$. Prove that $AN=CM$.