
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  $n$  be a positive integer. There are  $2018n+1$  cities in the Kingdom of Sellke Arabia. King Mark wants to build two-way roads that connect certain pairs of cities such that for each city  $C$  and integer  $1\le i\le 2018,$  there are exactly  $n$  cities that are a distance  $i$  away from  $C.$  (The *distance* between two cities is the least number of roads on any path between the two cities.)
    
For which  $n$  is it possible for Mark to achieve this?

*Proposed by Michael Ren*

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