
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 that $\left\{\begin{array}{l}x=2\\ y=1\end{array}\right.$ is a solution of the system of linear equations $\left\{\begin{array}{l}mx+ny=8\\ nx-my=1\end{array}\right.$, then the arithmetic square root of $2m-n$ is ______.

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