ELMO SL 2019 G4

Let triangle $ABC$ have altitudes $BE$ and $CF$ which meet at $H$ . The reflection of $A$ over $BC$ is $A'$ . Let $(ABC)$ meet $(AA'E)$ at $P$ and $(AA'F)$ at $Q$ . Let $BC$ meet $PQ$ at $R$ . Prove that $EF \parallel HR$ .

Proposed by Daniel Hu