
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In plane geometry, it is known that the area of the inscribed circle of a square is $S_1$, and the area of the circumscribed circle is $S_2$. Then $\dfrac{S_1}{S_2}=\left( \dfrac{1}{\sqrt{2}} \right)^2$. Extending this to three dimensions, for a cube with the volume of the inscribed sphere being $V_1$ and the volume of the circumscribed sphere being $V_2$, then $\dfrac{V_1}{V_2}=$_______.

Present the answer in LaTex format: \boxed{Your answer}
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