
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
Let \( f: \mathbf{Z} \rightarrow \mathbf{Z} \) be an even function such that \( f(1)=1 \) and \( f(2017) \neq 1 \). For any \( x, y \in \mathbf{Z} \), the following inequality holds:
$$
2 f(x+y)-f(x)-f(y) \leqslant|f(x)-f(y)|.
$$

Find all possible values of \( f(2018) \).

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