problem on Ceva's theorem

In quadrilateral $ABCD$ if $AB$ and $CD$ meet at $E$ and $AD$ and $BC$ at $F$ prove that midpoints of $DB, AC, FE$ are collinear.

My attempt: I connected the midpoints of $AC$ and $BD$ and assumed them to meet $FE$ at some point $Z$.

I tried to prove that $Z$ was mid point of $FE$ using Melenaus theorem but it only got complicated. how do I proceed?