
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 two-third sector of a circle with a radius of 6 inches is rolled into a cone by bringing the two radius ends together. Calculate the volume of the cone formed in cubic inches.
A) $\frac{48\pi \sqrt{3}}{3}$
B) $\frac{32\pi \sqrt{5}}{3}$
C) $\frac{24\pi \sqrt{7}}{3}$
D) $\frac{16\pi \sqrt{10}}{3}$

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