
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
The domain of the function \( f(x) \) is \(\mathbf{R}\), and for any \( x \in \mathbf{R} \), \( f(x) \neq -1 \) and \( f(x) \neq 0 \). Additionally, for any \( x, y \in \mathbf{R} \), \( f(x-y) = -\frac{f(x)}{1+f(y)} \). Is \( f(x) \) a periodic function? Why?

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