
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
In the parliament of the island nation Promenade-and-Tornado, 2019 native inhabitants have been elected, who are either knights or liars. Knights always tell the truth, and liars always lie. At the first session, 2016 of them sat in parliamentary chairs arranged in a rectangular hall of $42 \times 48$, and three sat in the chairs of the president and his deputies. During the session, each one claimed that among their neighboring chairs, there are both knights and liars (neighbors are those sitting left, right, front, back, and diagonally: there can be from 3 to 8 neighbors in the hall and 1 or 2 in the presidium). Determine the minimum number of liars at the session.

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