Problem 13 (2021 Fall AMC 12A)

In $\triangle ABC$ with $AB=25$, $AC=29$, and $BC=6$, the angle bisector of $\angle BAC$ intersects $BC$ at $D$. A circle is inscribed in $\triangle ABD$ and is tangent to $AB$ at $M$ and to $AD$ at $N$. What is $MN$?