
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 circle with radius $r$ has area $S(r) = \pi r^{2}$ and circumference $C(r) = 2\pi r$. If we consider $r$ as a variable on $(0, +\infty)$, then $(\pi r^{2})' = 2\pi r$. For a sphere with radius $R$, if we consider $R$ as a variable on $(0, +\infty)$, please write a similar expression: \_\_\_\_\_\_.

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