
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 equation \\((x^{2}-mx+2)(x^{2}-nx+2)=0\\), the four roots of the equation form a geometric sequence with the first term being \\( \frac {1}{2}\\). Find the absolute value of the difference between m and n, i.e., \\(|m-n|\\).

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