
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
Determine the number of ways to select a positive number of squares on an \(8 \times 8\) chessboard such that no two lie in the same row or the same column and no chosen square lies to the left of and below another chosen square.

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