
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 numbers \(1, 2, \ldots, 9\) are placed in a \(3 \times 3\) square. We will call such arrangements "feng shui" if for any choice of three cells, located in different columns and different rows, the sum of the numbers in the chosen cells is equal to 15. Find the number of all "feng shui" arrangements.

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