
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 number of quadratic polynomials \( P(x) = p_{1} x^{2} + p_{2} x - p_{3} \), where \( p_{1}, p_{2}, p_{3} \) are not necessarily distinct positive prime numbers less than 50, whose roots are distinct rational numbers.

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