
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
A function \( f: \mathbf{R} \rightarrow \mathbf{R} \) satisfies the property that for any real number \( x \),
\[ f(1-f(x)) = x. \]

(1) Provide a function \( f \) that meets this requirement.
(2) Determine all possible values of \( S_{f} = \sum_{k=-2017}^{2018} f(k) \).

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