
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 surface integral

$$
I=\int_{\Sigma}\left(\varphi \frac{\partial \psi}{\partial n}-\psi \frac{\partial \varphi}{\partial n}\right) d \sigma
$$

taken over the surface $\Sigma: x^{2}+y^{2}=R^{2}, z=0, z=H(H>0)$, if $\varphi=x^{2}+y^{2}+x+z, \psi=x^{2}+y^{2}+2 z+x$.

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