
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
Determine the positive difference between the roots of the quadratic equation $5x^2 - 9x + 1 = 0$. Express the difference in the form $\frac{\sqrt{p}}{q}$, where $p$ and $q$ are integers with $p$ not divisible by the square of any prime number. Compute $p + q$.

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