
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
Each of an ordered pair \( (b, c) \) of integers, where \( b \) and \( c \) have absolute values not exceeding four and \( c \) is non-zero, 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 have no real roots?
A) \(\frac{1}{2}\)
B) \(\frac{4}{9}\)
C) \(\frac{5}{9}\)
D) \(\frac{2}{3}\)
E) \(\frac{3}{4}\)

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