
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: \\(x^{2}+2ax-b^{2}+4=0\\),
(1) If \\(a\\) is a number randomly chosen from the set \\(\\{-1,0,1\\}\\), and \\(b\\) is a number randomly chosen from the set \\(\\{-3,-2,-1,0,1\\}\\), find the probability that the equation has real roots.
(2) If \\(a\\) is a number randomly chosen from the interval \\(\[-2,2\]\\), and \\(b\\) is a number randomly chosen from the interval \\(\[-2,2\]\\), find the probability that the equation has real roots.

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