
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
Twelve people sit around a circular table. Some of them are knights who always tell the truth, and the rest are liars who always lie. Each of the seated people declared the person sitting to their left to be a liar. Can it be definitively determined how many knights and how many liars are at the table?

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