
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 that $$f(x)+1= \frac {1}{f(x+1)}$$ and when $x \in [0, 1]$, $f(x)=x$. If $g(x)=f(x)-m$ has two distinct roots in the interval $(-1, 1]$, what is the range of the real number $m$?

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