
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
On an island, there are knights who always tell the truth and liars who always lie. At the main celebration, 100 islanders sat around a large round table. Half of the attendees said the phrase: "both my neighbors are liars," while the remaining said: "among my neighbors, there is exactly one liar." What is the maximum number of knights that can sit at this table?

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