
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
1. Find the particular integral of the equation \( y \, dx + \cot x \, dy = 0 \) that satisfies the initial condition \( y\left(\frac{\pi}{3}\right) = -1 \).
2. Solve the differential equation \( s = s' \cos^2 t \ln s \) with the initial condition \( s(\pi) = 1 \).

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