
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 side of the base of a regular triangular pyramid is equal to \(a\), and the height dropped from the vertex of the base to the opposite lateral face is \(b\). Find the volume of the pyramid.

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