
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
The diameter, in centimeters, of a sphere with three times the volume of a sphere of radius 5 centimeters can be expressed in the form $c\sqrt[3]{d}$ where $c$ and $d$ are positive integers and $d$ contains no perfect cube factors. Compute $c+d$.

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