
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 $f(x)=\begin{cases} \frac{1}{x+1}-3, & x\in(-1,0], \\ x, & x\in(0,1], \end{cases}$ and $g(x)=f(x)-mx-m$ has exactly two distinct zeros in $(-1,1]$, then the range of the real number $m$ is __________.

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