
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
Divide a circle into \( n \) (\( n \geqslant 2 \)) sectors \( S_{1}, S_{2}, \cdots, S_{n} \). There are \( m \) (\( m \geqslant 2 \)) colors available to color these sectors. Each sector is to be colored with exactly one color, and adjacent sectors must not have the same color. How many different coloring methods are there?

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