
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 length of the base of a regular triangular pyramid is \(a\), and the height dropped from the vertex of the base onto the opposite lateral face is \(b\). Determine the volume of the pyramid.

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