
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 line integral of the vector $\mathbf{a} = z \mathbf{i} + x \mathbf{j} + y \mathbf{k}$ along the arc $L$ of the helical line given by $x = R \cos t$, $y = R \sin t$, $z = \frac{t}{2 \pi}$ from point $A$, where the line intersects the plane $z = 0$, to point $B$, where it intersects the plane $z = I$.

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