
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 spherical coordinates: 

\[ 2 = e^{r} \sin \theta \mathbf{e}_{r} + 3 \theta^{2} \sin \varphi \mathbf{e}_{\theta} + \tau \varphi \theta \mathbf{e}_{\varphi} \]

along the line \( L: \left\{ r=1, \varphi=\frac{\pi}{2}, 0 \leqslant 0 \leqslant \frac{\pi}{2} \right\} \) in the direction from point \( M_{0}\left(1,0, \frac{\pi}{2}\right) \) to point \( M_{1}\left(1, \frac{\pi}{2}, \frac{\pi}{2}\right) \).

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