
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
We are placing rooks on a  $n \cdot  n$  chess table that providing this condition:
Every two rooks will threaten an empty square at least.
What is the most number of rooks?

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