
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 value of \( n \) if the roots of the equation \( 3x^2 - 7x + 4 = 0 \) can be expressed in the form \( x = \frac{m \pm \sqrt{n}}{p} \), where \( m \), \( n \), and \( p \) are integers with \( \gcd(m, n, p) = 1 \).

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