
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 $4 \times 4$ grid, each cell is filled with a unique number from $1$ to $16$. What is the probability that the sum of the numbers in each row and each column is even?
A) $\frac{71}{144}$
B) $\frac{72}{256}$
C) $\frac{1}{2}$
D) $\frac{1}{256}$
E) $\frac{36}{256}$

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