
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 the vector field:

a) \(\vec{A}=x y^{2} \vec{i}+x^{2} y \vec{j}+z^{3} \vec{k}\) at the point \( M(1,-1,3) \);

b) gradient of the function \(\varphi=x y^{2} z^{2}\);

c) \(\dot{A}=y z(4 x \vec{i}-y \vec{j}-z \vec{k})\).

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