MYTS 2016 - Grade 8 - Round 2 Question 6

In triangle $ABC$, let $D,E,F$ be the midpoints of $BC,CA,AB$, respectively. A line through $A$ meets $DE,DF$ at $M,N$, respectively. Let $P$ be the intersection of $BM$ and $CN$. Prove that $E,F,P$ are collinear.