
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 new tessellation composed of alternating rows of hexagons and triangles. A row of hexagons is followed by a row of triangles, such that each triangle touches exactly three hexagons, and each hexagon touches six triangles. What is the minimum number of colors needed to shade this tessellation, ensuring no two tiles sharing a side are the same color?

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