
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 $U = \mathbb{R}$, $A = \{x \mid |x - 2| > 1\}$, and $B = \{x \mid x \geq 0\}$, find $A \cap B$, $A \cup B$, and $(\mathbb{R} \setminus A) \cup B$.

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