ISL 2020 G2

Let $A B C D$ be a convex quadrilateral. Suppose that $P$ is a point in the interior of $A B C D$ such that $$\angle P A D: \angle P B A: \angle D P A=1: 2: 3=\angle C B P: \angle B A P: \angle B P C .$$ The internal bisectors of angles $A D P$ and $P C B$ meet at a point $Q$ inside the triangle $A B P$. Prove that $A Q=B Q$. (Poland)