
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
Fill the integers $1, 2, 3, 4, 5, 6, 7, 8, 9$ into a $3 \times 3$ grid, using each integer exactly once, so that the sum of the three numbers in each row and each column is odd. Determine the total number of such possible configurations.

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