
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
It is known that each side and diagonal of a regular polygon is colored in one of exactly 2018 different colors, and not all sides and diagonals are the same color. If a regular polygon contains no two-colored triangles (i.e., a triangle whose three sides are precisely colored with two colors), then the coloring of the polygon is called "harmonious." Find the largest positive integer $N$ such that there exists a harmonious coloring of a regular $N$-gon.

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