
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 chessboard is a $8 \times 8$ square where the squares are distributed in 8 rows and 8 columns.

A rook on a chessboard attacks all pieces that are in its row or in its column. Knowing this, determine:

a) What is the maximum number of rooks that can be placed on a chessboard so that no two rooks are attacking each other?

b) What is the maximum number of rooks that can be placed on a chessboard so that each rook is threatened by at most one of the other rooks?

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