
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
A circular wheel has 7 equal sections, and each of them will be painted with one of two colors. Two colorings are considered equivalent if one can be rotated to produce the other. In how many non-equivalent ways can the wheel be painted?

![Wheel Image](https://cdn.mathpix.com/cropped/2024_05_01_4fd1b602786ad9981479g-32.jpg?height=338&width=347&top_left_y=2028&top_left_x=736)

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