
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 $A=\{1,2\}$, $B=\{x\in \mathbb{R} | x^{2}-(a+1)x+a=0\}$. If the set $C=A\cup B$, and $C$ has $4$ subsets, then the set of possible real numbers for $a$ is ______.

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