
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 $A=\{x|2-a\leqslant x\leqslant 2+a\}$, $B=\{x|x\leqslant 1$ or $x\geqslant 4\}$.  
$(1)$ When $a=3$, find $A\cap B$;  
$(2)$ If $a > 0$, and $A\cap B=\varnothing$, find the range of the real number $a$.

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