
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 the system of linear equations in $x$ and $y$:
$$
\begin{cases}
ax+by=7 \\
bx+ay=8
\end{cases}
$$
The solution is:
$$
\begin{cases}
x=2 \\
y=3
\end{cases}
$$
Then, the solution for the system of linear equations in $m$ and $n$:
$$
\begin{cases}
a(m+n)+b(m-n)=7 \\
b(m+n)+a(m-n)=8
\end{cases}
$$
is _______.

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