
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 with wires such that each wire connects two phones, each pair of phones is connected by at most one wire, and each phone has at most two wires connected to it. We need to paint the wires (each wire entirely with one color) so that the wires connected to each phone are of different colors. What is the minimum number of colors needed for such painting?

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