
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
The squares of an  $8 \times 8$  board are coloured alternatingly black and white. A rectangle consisting of some of the squares of the board is called *important* if its sides are parallel to the sides of the board and all its corner squares are coloured black. The side lengths can be anything from  $1$  to  $8$  squares. On each of the  $64$  squares of the board, we write the number of important rectangles in which it is contained. The sum of the numbers on the black squares is  $B$ , and the sum of the numbers on the white squares is  $W$ . Determine the difference  $B - W$ .

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