
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 $A=\{x|x^{2}-2x-3 \gt 0\}$, $B=\{x|a-1 \lt x \lt 2a+3\}$.  
$(Ⅰ)$ If $a=-1$, find $(\complement _{R}A)\cap B$;  
$(Ⅱ)$ When $a=0$, does $A\cup B=R$ hold? Explain the reason;  
$(Ⅲ)$ Among the conditions $A\cup B=A$, $A\cap B=B$, $(\complement _{R}A)\cap B=\varnothing$, choose any one as the known condition, and find the range of real number $a$.  
(Note: If multiple conditions are chosen for separate answers, the first answer will be scored.)

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