
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 surface integral of the second kind:

$$
\iint_{S}\left(x y^{2}+z^{2}\right) d y d z+\left(y z^{2}+x^{2}\right) d z d x+\left(z x^{2}+y^{2}\right) d x d y
$$

where \( S \) is the exterior surface of the upper ( \(z \geq 0 \) ) hemisphere \( x^{2}+ y^{2}+z^{2}=a^{2} \).

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