
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

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

through the part of the surface

$$
x^2 + y^2 = 1
$$

bounded by the planes \( z = 0 \) and \( z = 2 \). (The normal vector is outward to the closed surface formed by these surfaces).

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