
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
On the squares of an $n \times n$ chessboard, there are hedgehogs on each square. Every second, the hedgehogs move to an adjacent diagonal square. What is the minimum number of squares that are occupied at all times?

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