
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
What is the maximum number of rooks that can be placed on a $300 \times 300$ chessboard so that each rook attacks no more than one other rook? (A rook attacks all the squares it can move to according to chess rules, without passing through other pieces.)

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