
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
You are allowed to cut out any 18 squares from a $20 \times 20$ chessboard, and after that, place several rooks on the remaining squares such that no two rooks attack each other. Rooks attack each other if they are in the same row or column of the board and there are no cut-out squares between them. What is the maximum number of rooks that can be placed under these conditions?

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