
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 differential equation:

$$
\left(1+x^{2}\right) d y - 2 x y d x = 0
$$

Find the particular solution that satisfies the condition \( y = 1 \) when \( x = 0 \).

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Find the general integral of the differential equation:

$$
\left(x y^{2}+x\right) d x+\left(y-x^{2} y\right) d y=0
$$

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