
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 cone if a chord of length \(a\) in its base subtends an arc of \(\alpha\) radians, and the height of the cone makes an angle \(\beta\) with the slant height.

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