In the rectangle $ABCD$, $BC = 5$, $EC = \frac{1}{3} CD$, and $F$ is the point where $AE$ and $BD$ intersect. The triangle $\triangle DFE$ has an area of $12$, and the triangle $\triangle ABF$ has an area of $27$. Find the area of the quadrilateral $BCEF$.

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