
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

$$
\iint_{S} x \, dy \, dz + y \, dz \, dx + z \, dx \, dy
$$

where \( S \) is the inner side of the ellipsoid \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}} = 1 \) for \( z \in [-H, H] \).

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