
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
Integrate the following equations:
1) $\left(x^{2}+y^{2}\right) d x-2 x y d y=0$
2) $y-x y^{\prime}=y \ln \frac{x}{y}$
3) $x d y-y d x=y d y$ given $y(-1)=1$.

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