
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]


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An equilateral triangle with side length \(a\) rotates around an axis passing through its vertex and forming an angle \(\varphi\) with one side. Find the volume \(V\) and surface area \(S\) of the resulting solid of revolution.

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