
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 infinite sheet of graph paper is painted with nine colors such that each cell is painted one color, and all the colors are used. We say two colors are neighboring if there are two cells with a common side painted in these colors. What is the smallest possible number of pairs of neighboring colors?

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