
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
You are given a chessboard with $n$ columns and $k$ rows. Some squares of the chessboard have disks placed on them (at most one per square). Two disks are called neighboring if they are in the same row or column, and there are no other disks between them along the line connecting them. Each disk has at most three neighbors. What is the maximum number of disks that can be on the chessboard?

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