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Let $F(x)$ be a non-decreasing function defined on $[0, 1 ]$ such that

$\begin{cases} 2 F \left ( \frac{x}{3} \right) = F(x), \\ F(x) + F(1-x) = 1 .\\ \end{cases}$

What is the value of $F ( \frac{1}{13} )$?

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