
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
Find the divergence of vector \(\vec{A}\), if:

a) \(\vec{A} = \frac{\vec{r}}{r}\) where \(r = \sqrt{x^{2}+y^{2}+z^{2}}\);

b) \(\vec{A} = -\frac{1}{\sqrt{x^{2}+y^{2}}}(x \vec{i} - y \vec{j} - z \vec{k})\).

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