
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 set $U={1,2,3,4,5,6,7,8}$, $A={x|x^{2}-3x+2=0}$, $B={x|1 \leqslant x \leqslant 5, x \in Z}$, $C={x|2 < x < 9, x \in Z}$.
Find (1) $A \cup (B \cap C)$; (2) $(U' \cap B) \cup (U' \cap C)$.

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