
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 7 natives seated in a circle: knights, liars, and bores (there is at least one representative of each tribe at the table). A knight always tells the truth, a liar always lies, and a bore lies if at least one knight is seated next to them; otherwise, the bore can say anything.

How many knights could there be at the table if, when asked "Who are your neighbors?" each native responded, "Both of my neighbors are bores"? Provide all possible scenarios and explain why no other scenarios are possible.

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