
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
Consider the following 4x4 matrix:
\[\left[\begin{matrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16 \end{matrix}\right]\]
All row sums and column sums are initially different. Determine the least number of entries that must be altered such that no two row sums or column sums are the same.
A) 0
B) 1
C) 2
D) 3
E) 4

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