
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
1. What is the chromatic number of the complete graph $\mathrm{K}_{4}$? More generally, what is the chromatic number of the complete graph $\mathrm{K}_{n}$?
2. What is the chromatic number of a square? Propose an optimal coloring.
3. Determine the chromatic numbers of the trees obtained in the solution of exercise 3.

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