
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
Suppose \( x^{3} - a x^{2} + b x - 48 \) is a polynomial with three positive roots \( p, q \), and \( r \) such that \( p < q < r \). What is the minimum possible value of \( \frac{1}{p} + \frac{2}{q} + \frac{3}{r} \)?

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