Let $$f : R \rightarrow R$$ be a continuous odd function, which vanishes exactly at one point and $$f(1) = \frac{1}{2}$$. Suppose that $$F(x) = \int_{-1}^{x} f(t) dt$$ for all $$x \in [-1, 2]$$ and $$G(x) = \int_{-1}^{x} t |f(f(t))| dt$$ for all $$x \in [-1, 2].$$ If $$\lim_{x \rightarrow 1} \frac {F(x)}{G(x)} = \frac{1}{14},$$ then the value of $$f \left(\frac{1}{2}\right)$$ is