
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
Consider the function \( f: \mathbb{N} \rightarrow \mathbb{Z} \) satisfying, for all \( n \in \mathbb{N} \),
(a) \( |f(n)| = n \)
(b) \( 0 \leq \sum_{k=1}^{n} f(k) < 2n \).
Evaluate \( \sum_{n=1}^{2018} f(n) \).

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