
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
In a class, there are $N$ students: several honor students and 8 bullies. Honor students always tell the truth, while bullies always lie.

One day, all the students in this class sat around a round table, and each of them declared to everyone else: "At least a third of you are bullies!"

What could be the value of $N$? List all possible options.

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