
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
If the augmented matrix of a system of linear equations in terms of $x$ and $y$ is $({\begin{array}{l}m&0\\ 0&3\end{array}\;\;\;\;\begin{array}{l}6\\ n\end{array}})$, and the solution of the system is $\left\{\begin{array}{l}x=-3\\ y=4\end{array}\right.$, then the value of $m+n$ is ____.

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