
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
Find particular solutions of the equation

$$
y^{\prime} \sin x = y \ln y
$$

satisfying the initial conditions:
a) \( y\big|_{x=\pi / 2} = e \);
b) \( y\big|_{x=\pi / 2} = 1 \).

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