Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>If $\overline{W P}$ is a median and an angle bisector, $A P=3 y+11$, $P H=7 y-5$, $m \angle H W P=x+12$, $m \angle P A W=3 x-2$, and $m \angle H W A=4 x-16$, find $x$.