
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 function $f(x)=\sqrt{(1-a^{2})x^{2}+3(1-a)x+6}$.  
$(Ⅰ)$ When $a=0$, find the range of $f(x)$;  
$(Ⅱ)$ If the domain of $f(x)$ is $\left[-2,1\right]$, find the value of the real number $a$;  
$(Ⅲ)$ If the domain of $f(x)$ is $R$, find the range of the real number $a$.

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