
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
Using the Ostrogradsky-Gauss theorem, compute the surface integral 
\[ I=\oiint_{+\sigma} \left( 4 x^{3} \, dy \, dz + 4 y^{3} \, dx \, dz - 6 z^{4} \, dx \, dy \right), \]
where \( \sigma \) is the complete surface of the cylinder as given in problem 906 (2).

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