
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 sets $A=\{x|x^{2}-2x-3\leqslant 0,x\in\mathbb{R}\}$, $B=\{x|(x-m+2)(x-m-2)\leqslant 0,x\in\mathbb{R},m\in\mathbb{R}\}$.  
$(1)$ If $A\cap B=\{x|0\leqslant x\leqslant 3\}$, find the value of the real number $m$;  
$(2)$ If $A\subseteq \complement_{\mathbb{R}}B$, find the range of the real number $m$.

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