Let $ABCDEF$ be a regular hexagon with $AB = 7$. Let $M$ be the midpoint of $DE$. The lines $AC$ and $BF$ intersect at $P$, $AC$ and $BM$ intersect at $Q$, and $AM$ and $BF$ intersect at $R$. Find the value of $[APB] + [BQC] + [ARF] - [PQMR]$, where $[X]$ denotes the area of polygon $X$.

Let's think step by step and output the final answer within \boxed{}.
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