
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 set $A=\{x\,|\,|x-2|\leq2\}$, where $x\in\mathbb{R}$, and $B=\{y\,|\,y=-x^2\}$, with $-1\leq x\leq 2$. Find the complement of $A\cap B$ in $\mathbb{R}$, denoted as $C_{\mathbb{R}}(A\cap B)$.

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