Let $S$ be the region bounded by the curves $y=x^3$ and $y^2=x$. The curve $y=2|x|$ divides $S$ into two regions of areas $\mathrm{R}_1$ and $\mathrm{R}_2$.
If $\max \left\{R_1, R_2\right\}=R_2$, then $\frac{R_2}{R_1}$ is equal to $\_\_\_\_$ .
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