
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
If a series of functions have the same analytical expression and range but different domains, they are called "functions of the same family". How many "functions of the same family" are there, given the analytical expression $y = x^2$ and the range $\{1, 2\}$?

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