
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 four row sums and the four column sums of the array 
\[\left[\begin{matrix}7 & 12 & 1 & 6 \\ 5 & 8 & 10 & 3 \\ 9 & 2 & 11 & 4 \\ 13 & 6 & 3 & 4\end{matrix}\right]\]
are the same. Determine the least number of entries that must be altered to make all eight sums different from one another?
A) 3
B) 4
C) 5
D) 6
E) 7

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