
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
Calculate the circulation of the vector field \( \mathbf{a} = y \mathbf{i} + z^{2} \mathbf{j} - z \mathbf{k} \) along the contour \( L: \left\{ \begin{array}{r} x^{2}+y^{2}=4, \\ z=3, \end{array} \right. \) 1) directly, 2) using Stokes' theorem.

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