
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 \(g : \mathbb{R} \to \mathbb{R}\) be a function such that
\[g(x) g(y) - g(xy) = x^2 + y^2\] for all real numbers \(x\) and \(y\).

Let \(m\) be the number of possible values of \(g(3)\), and let \(t\) be the sum of all possible values of \(g(3)\). Find \(m \times t\).

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