
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 $A=\{x \mid |x-2| \leq 2, x \in \mathbb{R}\}$, and $B=\{y \mid y=x^2-2x+2, 0 \leq x \leq 3\}$. Find the complement of $A \cap B$ in $\mathbb{R}$, denoted as $\complement_{\mathbb{R}}(A \cap B)$.

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