
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 real numbers $m$ and $n$ satisfying $m=\dfrac{\sqrt{n^{2}-4}+\sqrt{4-n^{2}}+4}{n-2}$, find the value of $|m-2n|+\sqrt{8mn}$.

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