
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 $U=\{x\in Z\mid -3\leqslant x\leqslant 3\}$, $A=\{1,2,3\}$, $B=\{-1,0,1\}$, $C=\{-2,0,2\}$, find:
$(1) A\cup(B\cap C)$;
$(2) A\cap\neg_{U}(B\cup C)$

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