
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 9 identical square rooms forming a $3 \times 3$ grid. Each of these rooms is occupied by one of 9 people: either liars or knights (liars always lie, knights always tell the truth). Each of these 9 people said: "At least one of my neighboring rooms has a liar." Rooms are considered neighbors if they share a wall. What is the maximum number of knights that could be among these 9 people?

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