
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
Draw a line parallel to one side of an equilateral triangle passing through one of its vertices. Determine the volume of the solid of revolution formed when the triangle is rotated about this line. The length of a side of the triangle is $a$.

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