
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 \(\mathbf{R}\). For any \( x \in (-\infty, +\infty) \), \( f(x+1) - f(x) = 1 \). Is the function \( F(x) = f(x) - x \) a periodic function, and why?

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