
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
Verify that the differential expression is a complete differential of a certain function \( u(x, y) \) and determine it:

a) \(\left(3x^2 y + 1\right) dx + \left(x^3 - 1\right) dy\)

b) \(y^2 e^{xy} dx + e^{xy}(1 + xy) dy\).

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