NMC 1993 Problem 1

Let $F$ be an increasing real function defined for all $x, 0 \leq x \leq 1$, satisfying the conditions

$$\begin{aligned} & F\left(\frac{x}{3}\right)=\frac{F(x)}{2} \\ & F(1-x)=1-F(x) \end{aligned}$$

Determine $F\left(\frac{173}{1993}\right)$ and $F\left(\frac{1}{13}\right)$.