
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 \( f : \mathbb{R} \to \mathbb{R} \) be a function such that
\[ f((x - y)^2 + 1) = f(x)^2 - 3xf(y) + y^2 \] for all real numbers \( x \) and \( y \).
Let \( n \) be the number of possible values of \( f(2) \), and let \( s \) be the sum of all possible values of \( f(2) \). Find \( n \times s \).

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