
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 the solid formed by the revolution of the curve  $ x \equal{} a(1 \plus{} \cos \theta )\cos \theta ,\ y \equal{} a(1 \plus{} \cos \theta)\sin \theta\ (a > 0,\ \minus{} \pi < \theta \leq \pi)$  about the  $ x$  axis.

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