
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 the universal set $U=A=\{x|x \text{ is a positive integer less than } 6\}$, $B=\{x|(x-1)(x-2)=0\}$, $C=\{a, a^2+1\}$,  
(1) Find $A \cap (\complement_{U} B)$, $A \cup B$;  
(2) If $B \subseteq C$, and $C \subseteq B$, find the value of the real number $a$.

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