
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
A half-circle sector of a circle with radius 6 inches, together with its interior, is rolled into the lateral surface of a right circular cone by joining the two radii ends. Determine the volume of the resulting cone.
A) $6\pi \sqrt{3}$ 
B) $9\pi \sqrt{3}$ 
C) $12\pi \sqrt{3}$ 
D) $18\pi \sqrt{3}$

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