$ABC$ is an acute angled scalene triangle. $L,M,N$ are midpoints of the sides $BC,CA,AB$.
The perpendicular bisectors of $\overline{AB}$ and $\overline{CA}$ meet $\overline{AL}$ at point $D$ and point $E$. The rays $\overrightarrow{BD}$ and $\overrightarrow{CE}$ cut each other at point $F$ inside the triangle.
Prove that $A,M,F,N$ are cyclic.
Tried by taking a point on symmedian and also tried by applying Menelaus theorem.
