9. (16 points) In the $x O y$ plane, draw two lines $A_{1} B_{1}$ and $A_{2} B_{2}$ through a point $P$ on the $x$-axis. Points $A_{1}$, $B_{1}$, $A_{2}$, and $B_{2}$ are all on the parabola $\Gamma: y^{2}=x$. Let $A_{1} B_{2}$ and $A_{2} B_{1}$ intersect the $x$-axis at points $S$ and $T$, respectively. Compare $\overrightarrow{O S} \cdot \overrightarrow{O T}$ with $|O P|^{2}$.