
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 2, 3, ..., 10 are randomly placed in the 9 squares of a 3 x 3 grid, with each square receiving one number and each number being used exactly once. Calculate the probability that the sum of the numbers in each row, each column, and both diagonals is odd and exceeds 15.

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