
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 flux of the vector field

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

through the surface

$$
x^{2}+y^{2}+z^{2}=9
$$

cut by the plane $z=0 \quad(z \geq 0)$ (outward normal to the closed surface formed by these surfaces).

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