
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 line integral of the second kind

$$
\int_{L} x^{2} y \, dx - y^{2} x \, dy
$$

where $L:\left(x^{2}+y^{2}\right)^{2}=a^{2}\left(x^{2}-y^{2}\right)^{2}, \ y \geqslant 0$ from $A(0,0)$ to $B(a, 0)$.

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