
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 integral \(I=\oint_{L} \frac{y}{x^{2}+y^{2}} dx - \frac{x}{x^{2}+y^{2}} dy\), where \(L\) is the circle:

a) \(x^{2} + y^{2} = 1\), b) \((x-1)^{2} + y^{2} = 1\), c) \((x-1)^{2} + (y-1)^{2} = 1\).

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