
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 flux of the vector field

$$
\vec{a}=-x \vec{i}+2 y \vec{j}+z \vec{k}
$$

through the portion of the plane

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

located in the first octant (the normal forms an acute angle with the $OZ$ axis).

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