
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
The function $f(x)=\sqrt{(1-a^2)x^2+3(1-a)x+6}$,<br/>$(1)$ If the domain of $f(x)$ is $\left[-2,1\right]$, find the value of the real number $a$.<br/>$(2)$ 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