2026 IMC keystage3-IWYMIC individual Question 15

In convex quadrilateral $ABCD$, $BD$ bisects $\angle ABC$. The circumcircle of $ABC$ meets $AD,CD$ again at $P,Q$. The line through $D$ parallel to $AC$ meets the extensions of $BC,AB$ at $R,S$. Prove $P,Q,R,S$ concyclic.