
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
Martin is playing a game. His goal is to place tokens on an 8 by 8 chessboard in such a way that there is at most one token per square, and each column and each row contains at most 4 tokens.

a) How many tokens can Martin place, at most?

b) If, in addition to the previous constraints, each of the two main diagonals can contain at most 4 tokens, how many tokens can Martin place, at most?

The main diagonals of a chessboard are the two diagonals running from one corner of the chessboard to the opposite corner.

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