
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
The lateral surface area of a regular triangular pyramid is three times larger than the area of its base. The area of the circle inscribed in the base is numerically equal to the radius of this circle. Find the volume of the pyramid.

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