
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 base of a pyramid is a triangle with sides of lengths \(a\), \(a\), and \(b\). All lateral edges are inclined at an angle of \(60^{\circ}\) to the plane of the base. Determine the volume of the pyramid.

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