
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
There are 100 people sitting in a circle. Some of them are knights who always tell the truth, while the others are liars who always lie. For some natural number \( k < 100 \), each person states: "The next \( k \) people sitting clockwise after me are liars." What values could \( k \) take?

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