
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
Given an ordered pair \( (b, c) \) of integers, each of which has absolute value less than or equal to seven, chosen randomly with each pair having an equal likelihood of being selected. What is the probability that the equation \( x^2 + bx + c = 0 \) will not have distinct positive real roots?
**A)** \( \frac{11}{15} \)
**B)** \( \frac{12}{15} \)
**C)** \( \frac{13}{15} \)
**D)** \( \frac{14}{15} \)
**E)** None of these

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