
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
Color the 3 vertices of an equilateral triangle with three colors: red, blue, and green. How many distinct colorings are there? Consider the following:

1. Colorings that can be made to coincide by rotation are considered identical.
2. Colorings that can be made to coincide by rotation and reflection are considered identical.

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