
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
A country is shaped like a square and is divided into 25 identical square counties. In each county rules 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 there could 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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