
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
Consider the quadratic equation \(3x^2 - 7x + 1 = 0\). The roots of this equation can be expressed in the form \(x = \frac{m \pm \sqrt{n}}{p}\), where \(m\), \(n\), and \(p\) are positive integers with a greatest common divisor of 1. Find the value of \(n\).

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