
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 $g$ be a function from integers to integers such that:
\[g(m + n) + g(mn - 1) = g(m) g(n) - 1\]
for all integers $m$ and $n.$ Determine the number of possible values for $g(3)$ and sum these values. Let $x$ be the number of these values and $y$ be their sum. Find $x \times y.$

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