
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 a $3 \times 3$ grid, the numbers $1, 2, ..., 9$ are randomly placed such that each number is used exactly once. Calculate the probability that the sum of the numbers in each row, each column, and along both main diagonals is odd.

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