
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
Consider an $n \times n$ square grid where $n$ is a fixed even positive integer. The grid is divided into $n^{2}$ unit squares. Two different squares in the grid are said to be adjacent if they share a common side.

In the grid, $N$ unit squares are marked in such a way that every square (whether marked or not) is adjacent to at least one marked square.

Determine the smallest possible value of $N$.

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