
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
The cells of a $9 \times 9$ board are colored in a checkerboard pattern with black and white colors (the corner cells are white). What is the minimum number of rooks that must be placed on this board so that all the white cells are under attack by these rooks? (A cell is under attack by a rook if it lies in the same row or column as the rook.)

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