
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
Given the function $f(x)=\begin{cases} x^{2}+2x, & x < 0 \\ \ln (x+1), & x\geq 0 \end{cases}$, if the equation $f(x)=x+m$ ($m\in \mathbb{R}$) has exactly three distinct real solutions, then the range of $m$ is $\boxed{(-\frac{1}{4},0)}$.

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