
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 \(I=\int_{\overparen{AB}}\left(x^{2}-2xy\right)dx + \left(y^{2}-2xy\right)dy\), where \(\overparen{AB}\) is the arc of the parabola connecting points \(A(-1,1)\) and \(B(1,1)\) and passing through the origin.

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