
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
An ordered pair \((b, c)\) of integers, each of which has an absolute value not exceeding ten, is chosen at random. Each such ordered pair has an equal likelihood of being chosen. What is the probability that the equation \(x^2 + bx + c = 0\) will not have distinct positive real roots?
A) $\frac{400}{441}$
B) $\frac{401}{441}$
C) $\frac{411}{441}$
D) $\frac{421}{441}$

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