
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
Construct a section on a sphere with an area equal to one-third of the area of a great circle, and place a cone on this section such that its apex is at the center of the sphere. If the volume of the cone is $480 \mathrm{~m}^{3}$, what will be the radius of the sphere?

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