
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 the particular solution of the equation $\left(1+e^{x}\right) y y^{\prime}=\mathrm{e}^{x}$, satisfying the initial condition $\left.y\right|_{x=0}=1$.

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