
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 two positive integers such that $\frac{n}{2}<k \leq \frac{2n}{3}$. We place $m$ pieces on a chessboard of size $n \times n$ such that no row or column contains a block of $k$ empty squares. What is the smallest integer $m$ for which this is possible?

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