There is a rectangle $ABCD$ such that $AB = 12$ and $BC = 7$. Points $E$ and $F$ lie on sides $AB$ and $CD$, respectively, such that $\frac{AE}{EB} = 1$ and $\frac{CF}{FD} = \frac{1}{2}$. Let $X$ be the intersection of lines $AF$ and $DE$. What is the area of pentagon $BCFXE$?

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