
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 sets $A=\{x|x^{2}-2x-3\leqslant 0\}$ and $B=\{x\left|\right.\left(x-m+1\right)\left(x-m-1\right) \gt 0\}$.  
$(1)$ When $m=0$, find $A\cap B$;  
$(2)$ If $x\in B$ is a necessary but not sufficient condition for $x\in A$, find the range of real numbers for $m$.

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