
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 an $8 \times 8$ chessboard, some squares are marked with asterisks such that:
(1) No two squares with asterisks share a common edge or vertex;
(2) Every unmarked square shares a common edge or vertex with at least one marked square.

What is the minimum number of squares that need to be marked with asterisks? Explain the reasoning.

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