
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 given line integrals of the second kind:

a) $\int_{L} 2 y \sin 2 x \, dx - \cos 2 x \, dy$, where $L$ is any piecewise smooth curve connecting the points $A\left(\frac{\pi}{2}, 2\right)$ and $B\left(\frac{\pi}{6}, 1\right)$.

b) $\int_{L} y x e^{x} \, dx - (x-1) e^{x} \, dy$, where $L$ is any piecewise smooth curve connecting the points $A(0,2)$ and $B(1,2)$.

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