
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 only knights, who always tell the truth, and liars, who always lie. One fine day, 450 islanders sat at a round table. Each person at the table said: "Of the person sitting to my right and the one immediately next to him, exactly one is a liar." How many liars can be sitting at the table?

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