
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 $A$ be the set of all real numbers $a$ that satisfy $\left(a-2\right)x^{2}+2\left(a-2\right)x-4 \lt 0$ for any $x\in R$. Let $B$ be the set of all real numbers $x$ that satisfy $\left(a-2\right)x^{2}+2\left(a-2\right)x-4 \lt 0$ for any $a\in \left[-2,2\right]$. Find $A\cap (\complement _{R}B)$.

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