
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 $U=\{1,2,3,4,5,6,7,8\}$, $A=\{x|x^2-3x+2=0\}$, $B=\{x|1\leq x\leq 5, x\in \mathbb{Z}\}$, $C=\{x|2<x<9, x\in \mathbb{Z}\}$. (Please use the enumeration method for the following)
(1) Find the intersection of set A and set B
(2) Find $A\cup (B\cap C)$
(3) Find $(\complement_U B) \cup (\complement_U C)$.

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