
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  $2024$  people, which are knights and liars and some of them are friends. Every person is asked for the number of their friends and the answers were  $0,1, \ldots, 2023$ . Every knight answered truthfully, while every liar changed the real answer by exactly  $1$ . What is the minimal number of liars? 

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