
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
Given a set of functions described by the same analytical expression and having the same range but different domains, these functions are called "homologous functions." How many "homologous functions" are there with the analytical expression $y=x^2$ and the range $\{1, 4\}$?

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