
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
Find the volume of a regular quadrilateral pyramid whose base sides are of length \(a\), and the planar angles at the apex are equal to the angles of inclination of the lateral edges to the base plane.

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