
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 $p$: Real number $x$ satisfies the set $A=\{x|a-1\leqslant x\leqslant a+1\}$, $q$: Real number $x$ satisfies the set $B=\{x|x\leqslant -2$ or $x\geqslant 3\}$.  
$(1)$ If $a=-2$, find $A\cap B$;  
$(2)$ If $p$ is a sufficient but not necessary condition for $q$, find the range of real number $a$.

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