
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 where each square must be filled with a unique number from $1$ to $9$, calculate the probability that both the sum of the numbers in each row and the sum of the numbers in each column will be odd.

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