
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
Given the quadratic equation in x, x² + 2ax + b² = 0, where a and b are random numbers within a certain range, find the probability that the equation has real roots under the following conditions:

1. If the random numbers a and b belong to the set {1, 2, 3, 4, 5, 6};
2. If a is any number from the interval [0, 5], and b is any number from the interval [2, 4].

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