
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
Let $U = \{x \in \mathbb{Z} | -3 \leq x \leq 3\}$, $A = \{1, 2, 3\}$, $B = \{-1, 0, 1\}$, and $C = \{-2, 0, 2\}$.  
Find: (1) $A \cup (B \cap C)$;  
(2) $A \cap \complement_U (B \cup C)$

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