
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 equations of the form \( x^2 + bx + c = 0 \). How many such equations have real roots if coefficients \( b \) and \( c \) are selected from the sets \( B = \{2, 4, 6\} \) and \( C = \{1, 3, 5\} \), respectively?

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