
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
Let \( f(r) \) be an arbitrary differentiable function (\( f(r) \in C^{1}(\mathbb{R}) \)). Determine when

a) \( \operatorname{div}(\operatorname{grad} f(r))=0 \) where \( r=\sqrt{x^{2}+y^{2}+z^{2}} \);

b) \( \operatorname{div}(f(r) \cdot \dot{r})=0 \).

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