
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
Let the universal set be $R$, set $A=\{x|x \lt -2$ or $x \gt 3\}$, $B=\{x|1-a \lt x \lt a+3\}$.  
$(1)$ If $a=1$, find $(\complement _{R}A)\cup B$;  
$(2)$ Given $A\cap B=\varnothing$, find the range of real number $a$.

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