
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 set $A = \{x \mid x \text{ is a positive integer less than 6}\}$, $B = \{x \mid (x-1)(x-2)=0\}$, $C=\{a, a^2+1\}$,
(Ⅰ) Find $A \cap B$, $A \cup B$;
(Ⅱ) 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