Let $f: R \rightarrow R$ be a continuous odd function, which vanishes exactly at one point and $f(1)=\frac{1}{2}$. Suppose that $F(x)=\int_{-1}^x f(t) d t$ for all $x \in[-1,2]$ and $G(x)=\int_{-1}^x t|f(f(t))| d t$ 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.