Australian Intermediate Mathematics Olympiad 2018 Question 6

Let $ABCD$ be a parallelogram. Point $P$ is on $AB$ produced so that $DP$ bisects $BC$ at $N$. Point $Q$ is on $BA$ produced so that $CQ$ bisects $AD$ at $M$. Lines $DP$ and $CQ$ meet at $O$. If $[ABCD]=192$, find $[POQ]$.