
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 $1,2,\dots,9$ are randomly placed into the $9$ squares of a $3 \times 3$ grid. Each square gets one number, and each of the numbers is used once. What is the probability that the sum of the numbers in each row, each column, and the main diagonal (from the top left to the bottom right) is odd?
A) $\frac{1}{63}$
B) $\frac{1}{120}$
C) $\frac{1}{126}$
D) $\frac{1}{252}$
E) $\frac{1}{14}$

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