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

Hence, the correct answer is 7.