
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
\[ A=\left(\frac{4 m^{2} n^{2}}{4 m n-m^{2}-4 n^{2}}-\frac{2+\frac{n}{m}+\frac{m}{n}}{\frac{4}{m n}-\frac{1}{n^{2}}-\frac{4}{m^{2}}}\right)^{1 / 2}: \frac{\sqrt{m n}}{m-2 n} \]

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