
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
a) Consider a $6 \times 6$ chessboard. What is the minimum number of kings that can be placed on the board so that all squares are either occupied or attacked by one of the kings?

b) Still considering the $6 \times 6$ chessboard, what is the maximum number of kings that can be placed on the board such that no kings attack each other?

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