
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
(12 points) Given the sets $A=\{x|a-2<x<a+2\}$, $B=\{x|x^2-(a+2)x+2a=0\}$, where $a\in \mathbb{R}$.  
(1) If $a=0$, find the value of $A\cup B$;  
(2) If $(\mathbb{R}\setminus A) \cap B \neq \emptyset$, find the range of values for $a$.

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