
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
20 phones are connected by wires such that each wire connects two phones, no pair of phones is connected by more than one wire, and no more than two wires come out of each phone. The wires need to be colored (each wire entirely one color) so that the wires coming out of each phone are of different colors. What is the minimum number of colors required for such a coloring?

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