
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
Given an \( n \times n \) square board divided into \( n^2 \) unit squares, where two squares are considered adjacent if they share a common edge, find the minimum number \( N \) of marked unit squares such that every unit square (whether marked or unmarked) is adjacent to at least one marked square.

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