
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 right circular cone has a height equal to twice the radius of a given sphere. Find the ratio of the cone's volume to that of the sphere when the base's radius of the cone is the same as the sphere's radius.
A) $\frac{1}{4}$  
B) $\frac{1}{2}$  
C) $\frac{3}{4}$  
D) $\frac{3}{2}$

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