RU-ORAL-GEOMETRY 2018 Problem 3

On the extensions of sides $CA$ and $AB$ of triangle $ABC$ beyond points $A$ and $B$ , respectively, the segments $AE = BC$ and $BF = AC$ are drawn. A circle is tangent to segment $BF$ at point $N$ , side $BC$ and the extension of side $AC$ beyond point $C$ . Point $M$ is the midpoint of segment $EF$ . Prove that the line $MN$ is parallel to the bisector of angle $A$ .