
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 $U=\{1,2,3,4,5,6,7,8\}$, $A=\{x \mid x^2-3x+2=0\}$, $B=\{x \mid 1 \leq x \leq 5, x \in \mathbb{Z}\}$, $C=\{x \mid 2 < x < 9, x \in \mathbb{Z}\}$.
(1) Find $A \cup (B \cap C)$.
(2) Find $(\complement_{U}B) \cup (\complement_{U}C)$.

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