
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 $g(x)= \begin{cases}\frac {1}{x+1}-3, & -1 < x\leqslant 0 \\ x^{2}-3x+2, & 0 < x\leqslant 1\end{cases}$, if the equation $g(x)-mx-m=0$ has exactly two distinct real roots, then the range of the real number $m$ is \_\_\_\_\_\_.

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