
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 a 4x4 matrix:
\[
\left[\begin{matrix}
5 & 11 & 3 & 6\\
12 & 2 & 7 & 4\\
8 & 6 & 9 & 2\\
10 & 3 & 1 & 11
\end{matrix}\right]
\]
Determine the least number of entries that must be altered to ensure that all row sums, column sums, and the main diagonal sum are different from one another.

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