
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
Randomly choose any pair of ordered integers \((b, c)\), where the absolute value of each integer is less than or equal to 5. Each such pair of ordered integers is equally likely to be chosen. Determine the probability that the equation \(x^2 + bx + c = 0\) does not have two distinct positive real roots.

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