
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
An office is equipped with 2004 telephones, where any two telephones are connected by a wire of one of 4 colors. Knowing that all four colors of wire are used, find if it is always possible to identify a set of telephones such that the wires connecting them have exactly three different colors.

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