
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 equation of a circle \\((x-a)^{2}+(y-b)^{2}=r^{2}(r > 0)\\), choose 3 different numbers from \\(0, 3, 4, 5, 6, 7, 8, 9, 10\\) to be the x-coordinate of the center, the y-coordinate of the center, and the radius of the circle, respectively. Answer the following questions:  
\\((1)\\) How many different circles can be formed?  
\\((2)\\) How many of these circles pass through the origin?  
\\((3)\\) How many of these circles have their centers on the line \\(x+y-10=0\\)?

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