
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
We entered the natural numbers from 1 to 9 into a $3 \times 3$ table. We know that no matter how we choose three numbers, none of which are in the same row or column, their sum is always 15. How many such tables are there?

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