
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
Let  $ n$  and  $ k$  be positive integers such that  $ \frac{1}{2} n < k \leq \frac{2}{3} n.$  Find the least number  $ m$  for which it is possible to place  $ m$  pawns on  $ m$  squares of an  $ n \times n$  chessboard so that no column or row contains a block of  $ k$  adjacent unoccupied squares.

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