
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 $n(\geqslant 2)$ sectors $S_{1}, S_{2}, \cdots, S_{n}$. Using $m(\geqslant 2)$ colors, color these sectors such that each sector is colored with one color and no two adjacent sectors share the same color. How many different ways of coloring are there?

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