
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
Calculate the positive difference between the roots of the quadratic equation \(2x^2 - 10x + 3 = 0\). Express the difference in a simplified radical form, and find the sum \(m + n\) where the difference is represented as \(\frac{\sqrt{m}}{n}\), \(m\) is an integer not divisible by the square of any prime number, and \(n\) is an integer.

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