IR-TST 2020 Problem 2

Let $O$ be the circumcenter of the triangle $ABC$ . Points $D,E$ are on sides $AC,AB$ and points $P,Q,R,S$ are given in plane such that $P,C$ and $R,C$ are on different sides of $AB$ and pints $Q,B$ and $S,B$ are on different sides of $AC$ such that $R,S$ lie on circumcircle of $DAP,EAQ$ and $\triangle BCE \sim \triangle ADQ , \triangle CBD \sim \triangle AEP$ (In that order), $\angle ARE=\angle ASD=\angle BAC$ , If $RS\| PQ$ prove that $RE ,DS$ are concurrent on $AO$ .

Proposed by Alireza Dadgarnia