
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 $A=\{x|2x^2+ax+2=0\}$, and $B=\{x|x^2+3x+2a=0\}$, with $A\cap B=\{2\}$.

(1) Find the value of $a$ and the sets $A$, $B$;  
(2) Let the universal set $U=A\cup B$, find $(\complement_U A) \cup (\complement_U B)$;  
(3) List all subsets of $(\complement_U A) \cup (\complement_U B)$.

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