
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 an $8 \times 8$ grid, each cell contains either a knight or a knave. Knights always tell the truth, and knaves always lie. Every resident in the grid states: "The number of knaves in my column is strictly greater than the number of knaves in my row." Determine the number of possible arrangements of residents that satisfy this condition.

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