
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) What is the maximum number of knights that can be placed on a chessboard of 64 squares so that no two knights threaten each other?

b) Determine the number of different arrangements of the maximum possible number of knights where no two knights threaten each other.

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