
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 the functions $f(x)$ and $g(x)$ satisfy: $g(x-y) = g(x)g(y) + f(x)f(y)$; with $f(-1) = -1$, $f(0) = 0$, $f(1) = 1$, find the values of $g(0)$, $g(1)$, and $g(2)$.

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