
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

Compute the line integral of the vector field given in cylindrical coordinates \( \mathbf{F} = 4\rho \sin \varphi \mathbf{e}_{\rho} + z e^{p} \mathbf{e}_{,\varphi} + (\rho + \varphi) \mathbf{e}_{z} \) along the line \( L: \left\{\varphi=\frac{\pi}{4}, z=0\right\} \) from the point \( O\left(0, \frac{\pi}{4}, 0\right) \) to the point \( A\left(1, \frac{\pi}{4}, 0\right) \).

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