
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 integral \( I = \iint_{\sigma} \left( x \cos \alpha + \cos \beta + x z^{2} \cos \gamma \right) d \sigma \), where \(\sigma\) is the part of the sphere \( x^{2} + y^{2} + z^{2} = 1 \) located in the first octant.

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