Let $f : \mathbb { R } \rightarrow \mathbb { R }$ 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