
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 circulation of the vector field

$$
\vec{a}=y \vec{i}-x z \vec{j}+x y \vec{k}
$$

along the closed contour

$$
\Gamma=\left\{(x, y, z): \begin{array}{l}
x^{2}+y^{2}+z^{2}=9 \\
x^{2}+y^{2}=9
\end{array}\right\}
$$

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