
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 **F** = (x - 2y + 1)i + (2x + y - 3z)j + (3y + z)k through the part of the surface of the sphere x² + y² + z² that lies in the first octant in the region where x² + y² + z² > 1.

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