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>In quadrilateral $A B C D, A C=188, B D=214$, $m \angle B P C=70,$ and $P$ is the midpoint of $A C$ and BD. Find the perimeter of quadrilateral $A B C D .$