
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
In each cell of an \(8 \times 8\) square, one of the diagonals is drawn. Consider the union of these 64 diagonals. It consists of several connected parts (points belong to the same part if they can be traversed through one or more diagonals). Can the number of these parts be

a) greater than 15?

b) greater than 20?

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