
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 square board with  $8\text{cm}$  sides is divided into  $64$  squares square with each side  $1\text{cm}$ . Each box can be painted white or black. Find the total number of ways to colour the board so that each square of side  $2\text{cm}$  formed by four squares with a common vertex contains two white and two black squares.

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