
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
Let  $ p \geq 3$  be a prime, and let  $ p$  points  $ A_{0}, \ldots, A_{p-1}$  lie on a circle in that order. Above the point  $ A_{1+\cdots+k-1}$  we write the number  $ k$  for  $ k=1, \ldots, p$  (so  $ 1$  is written above  $ A_{0}$ ). How many points have at least one number written above them?

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