SMO 2016 Senior Round 2 Question 1

In a triangle $ABC$, $M$ is the midpoint of $BC$ and $D$ is the point on $BC$ such that $AD$ bisects $\angle BAC$. The line through $B$ perpendicular to $AD$ intersects $AD$ at $E$ and $AM$ at $G$. Prove that $GD$ is parallel to $AB$.