
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 $f(x)= \begin{cases} -x+m, & x < 0\\ x^{2}-1, & x\geqslant 0 \end{cases}$ where $m > 0$, if the function $y=f(f(x))-1$ has $3$ different zeros, then the range of $m$ is \_\_\_\_\_.

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