
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
The arrangement of chess kings on a board is called "correct" if none of them attack each other, and every square of the board is either under attack or occupied by one of the kings. What is the minimum and maximum number of kings that can be correctly placed on an $8 \times 8$ chessboard?

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