
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
Given a 4x4 matrix:
\[
\left[\begin{array}{cccc}
1 & 15 & 14 & 4 \\
12 & 6 & 7 & 9 \\
8 & 10 & 11 & 5 \\
13 & 3 & 2 & 16
\end{array}\right]
\]
what is the least number of entries that must be changed to make all ten sums different from one another?

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