
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 a quadratic equation in \\(x\\), \\(x^{2}-2(a-2)x-b^{2}+16=0\\)  
\\((1)\\) If the numbers obtained from rolling a die twice are \\(a\\) and \\(b\\), respectively, find the probability that the equation has two positive roots;  
\\((2)\\) If \\(a \in [2,6]\\) and \\(b \in [0,4]\\), find the probability that the equation has no real roots.

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