
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
Consider a tessellation made up of regular hexagonal tiles, each of which shares sides with three to six neighbors depending on its position in the grid. What is the least number of colors needed to shade this tessellation such that no two tiles sharing a side are the same color?

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