
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
Compute the surface integral

$$
\iint_{\Sigma}(-x+3 y+4 z) d \sigma
$$

where $\Sigma$ is the part of the plane

$$
x + 2y + 3z = 1
$$

located in the first octant (i.e., $x \geq 0, y \geq 0, z \geq 0$).

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