
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 the universal set $U={x|x^2-3x+2\geqslant 0}$, set $A={x||x-2| > 1}$, and set $B={x| \frac{x-1}{x-2} > 0}$. Find: (1) $A \cap B$; (2) $A \cap \lnot_{U} B$; (3) $\lnot_{U}(A \cup B)$.

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