
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
The country is shaped like a square and is divided into 25 identical square counties. In each county, there is either a knight count, who always tells the truth, or a liar count, who always lies. One day, each count said: "Among my neighbors, there are an equal number of knights and liars." What is the maximum number of knights that could possibly be? (Counts are considered neighbors if their counties share a common side.)

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