
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
If the functions \( f(x) \) and \( g(x) \) are defined on \( \mathbf{R} \), and \( f(x-y)=f(x)g(y)-g(x)f(y) \), with \( f(-2)=f(1) \neq 0 \), what is \( g(1) + g(-1) \)?

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