
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
Given that a circle is divided into six equal sections, three of which are red, one is blue, one is green, and one is yellow, and two circles are considered the same if one can be rotated to match the other, find the number of different colourings for the circle.

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