
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 $U=\{x\in Z||x| \lt 3\}$, $A=\{0,1,2\}$, $B=\{1,2\}$.  
$(1)$ Find $A\cup B$;  
$(2)$ Find $(\complement _{U}A)\cap (\complement _{U}B)$.

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