Question 180
In $\triangle PMO$, $PM = 6\sqrt{3}$, $PO = 12\sqrt{3}$, and $S$ is a point on $MO$ such that $PS$ is the angle bisector of $\angle MPO$. Let $T$ be the reflection of $S$ across $PM$. If $PO$ is parallel to $MT$, find the length of $OT$.