
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
Given a regular polygon where each side and each diagonal is colored in one of 2018 different colors, and no two sides or diagonals are all the same color. A coloring is called "harmonious" if there are no two-colored triangles in the polygon (i.e., no triangle where exactly two of the three sides are the same color). Find the largest positive integer $N$ for which there exists a harmonious coloring for a regular $N$-gon.

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