
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 the right triangular prism $ABC-A_{1}B_{1}C_{1}$ with a volume of $3\sqrt{7}$, where $AB=2$ and $AC=3$, the minimum value of the surface area of the circumscribed sphere of this prism is ______.

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