
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
Consider  $n$  points  $A_1, A_2, \ldots, A_n$  on a circle.  How many ways are there if we want to color these points by  $p$  colors, so that each two neighbors points are colored with two different colors?

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