
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
Given the numbers $1, 2, \dots, 16$ are randomly placed into the $16$ squares of a $4 \times 4$ grid, where each square receives one number and each number is used once, calculate the probability that the sum of the numbers in each row and each column is odd.

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