
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
A nearsighted rook attacks all cells in its row and column that can be reached within 60 steps, moving from one cell to an adjacent cell. What is the maximum number of non-attacking nearsighted rooks that can be placed on a $100 \times 100$ grid?

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