Equilateral triangle $ABC$ has area $1$. $A'$, $B'$, and $C'$ are the midpoints of $BC$, $CA$, and $AB$, respectively. $A''$, $B''$, $C''$ are the midpoints of $B'C'$, $C'A'$, and $A'B'$, respectively. The area of trapezoid $BB''C''C$ can be written as $\frac{m}{n}$ for relative prime positive integers $m$ and $n$. Find $m+n$.

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