
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
Calculate the line integral

$$
J = \int_{C}(2 x + 4 z) \, dx + (2 y + 2 z) \, dy - 12 z \, dz
$$

along one turn of the helix \(C\):

$$
\begin{aligned}
& x = 2 \cos 4t, \\
& y = 2 \sin 4t, \\
& z = 6t, \quad 0 \leq t \leq 2\pi
\end{aligned}
$$

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