
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
The Four Color Problem states that it is possible to color any map using no more than four colors such that no two adjacent countries (countries that share a common boundary segment) have the same color. Countries that only share a boundary at a single point are not considered adjacent. 

Provide a proof that any map can indeed be colored with four or fewer colors under these conditions.

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