
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 sphere's diameter in inches that has three times the volume of a sphere with a radius of 6 inches can be calculated in the form \(a\sqrt[3]{b}\) where \(a\) and \(b\) are positive integers, and \(b\) has no perfect cube factors. Compute \(a+b\).

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