
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
All three row sums and the three column sums of the matrix \[
\left[\begin{matrix}
5 & 10 & 3\\ 
9 & 2 & 8\\ 
4 & 6 & 9
\end{matrix}\right]
\]
are identical; find the minimum number of entries that must be altered to ensure all six sums (three row sums and three column sums) differ from each other.

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