
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 16 positive integers from 1 to 16 are randomly placed into the 16 squares of a 4x4 chessboard, with each square containing exactly one number. What is the probability that the sum of the numbers in each row and each column is even?

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