
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
Check if the field \(\dot{A}\) is solenoidal \((\operatorname{div} \dot{A}=0)\). If yes, then find its vector potential:

a) \(\dot{A}=(y+z) \dot{i}+(x+z) \vec{j}+(x+y) \vec{k}\);

b) \(\dot{A}=y e^{x^{2}} \dot{i}+2 y z \dot{j}-\left(2 x z y e^{x^{2}}+z^{2}\right) \ddot{k\).

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