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

a) through the lateral surface of the cylinder $x^{2} + y^{2} \leqslant R^{2}$, $|z| \leqslant H$ (normal is outward);

b) through the lateral surface of the cone $x^{2} + y^{2} \leqslant 4z^{2}$, $z \in [0,1]$ (normal is inward);

c) through the entire surface of the cube $|x| \leqslant a, |y| \leqslant a, |z| \leqslant a$ (normal is outward).

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