
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 3x3 matrix given by 
\[\left[\begin{matrix} x & 9 & y\\ 8 & z & 6\\ 3 & 5 & 7\end{matrix}\right]\]
where \(x\), \(y\), and \(z\) are integers. If initially $x=4$, $y=2$, and $z=1$, which results in every row and column sum being 15, how many variable entries should be changed to ensure all row and column sums are different?
A) 2
B) 3
C) 4
D) 5
E) 6

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