IR-TST 2023 Problem 6

$ABC$ is an acute triangle with orthocenter $H$ . Point $P$ is in triangle $BHC$ that $\angle HPC = 3 \angle HBC$ and $\angle HPB =3 \angle HCB$ . Reflection of point $P$ through $BH,CH$ is $X,Y$ . if $S$ is the center of circumcircle of $AXY$ , Prove that: $$\angle BAS = \angle CAP$$ Proposed by Pouria Mahmoudkhan Shirazi