
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

In some cells of a $10 \times 10$ board, $k$ rooks are placed, and then all the cells that are attacked by at least one rook are marked (a rook attacks the cell it is on). What is the maximum value of $k$ such that, if any one rook is removed from the board, there will still be at least one marked cell that is not under attack?

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