
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
There is a sheet of graph paper. Each grid node is marked with a certain letter. What is the minimum number of different letters required to mark these nodes so that on any line segment connecting two nodes marked with the same letter, there is at least one node marked with one of the other letters?

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