
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
Find the number of functions \(g : \mathbb{R} \to \mathbb{R}\) such that
\[g(x + y) g(x - y) = (g(x) - g(y))^2 - 6x^2 g(y)\] for all real numbers \(x\) and \(y.\)

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