
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 a quadratic equation \( x^2 + bx + c = 0 \) where \( b \) and \( c \) are integers such that \( -10 \leq b \leq 10 \) and \( -10 \leq c \leq 10 \). Each ordered pair \((b, c)\) is equally likely. Find the probability that the equation will not have distinct real roots with the sum of roots equal to \( -b \) being positive.
**A)** \( \frac{37}{441} \)
**B)** \( \frac{404}{441} \)
**C)** \( \frac{100}{441} \)
**D)** \( \frac{110}{441} \)
**E)** None of these

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