
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 the island of Unfortune, there live knights who always tell the truth and liars who always lie. One day, 2022 natives gathered at a round table, and each of them made the statement:

"Next to me sit a knight and a liar!"

It is known that three knights made a mistake (i.e., unintentionally lied). What is the maximum number of knights that could have been at the table?

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