
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 a castle, there are 16 identical square rooms arranged in a $4 \times 4$ grid. Each of these rooms is occupied by one person, making a total of 16 people, who are either liars or knights (liars always lie, knights always tell the truth). Each of these 16 people said: "There is at least one liar in one of the rooms adjacent to mine." Two rooms are considered adjacent if they share a wall. What is the maximum number of liars that could be among these 16 people?

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