
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 natural number  $n\geqslant 2$ , find the smallest possible number of edges in a graph that has the following property: for any coloring of the vertices of the graph in  $n{}$  colors, there is a vertex that has at least two neighbors of the same color as itself.

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