
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 five-eighths sector of a circle with a radius of 5 inches is rolled up to form the lateral surface area of a right circular cone. What is the volume of the cone in cubic inches?
A) $10\pi$ cubic inches
B) $12\pi$ cubic inches
C) $12.66\pi$ cubic inches
D) $15\pi$ cubic inches

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