
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
Given that the upper and lower base radii of the frustum $O_{1}O_{2}$ are $\sqrt{3}$ and $3\sqrt{3}$ respectively, if there exists a sphere that is tangent to the upper and lower bases as well as the lateral surface of the frustum simultaneously, then the volume of the frustum is ______.<br/>Note: The formula for the volume of a frustum is: $V=\frac{1}{3}({S}_{top}+\sqrt{{S}_{top}{S}_{bottom}}+{S}_{bottom})h$

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