
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 $A=\{x|x^{2}-2x-3\leqslant 0\}$, $B=\{x\left|\right.a-1\leqslant x\leqslant 2a+1\}$, $a\in R$.  
$(1)$ When $a=1$, find $A$⋃$B$ and $\complement _{R}B$;  
$(2)$ If $(\complement _{R}A)$⋂$B=\varnothing$, find the range of real number $a$.

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