
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 cone has a radius of 2 inches and a height of 6 inches. The cone's material is twice as dense as the sphere's material. If the cone and the sphere have the same physical volume, what is the radius of the sphere?

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