
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 circle \\(O\\): \\(x^{2}+y^{2}=r^{2}(r > 0)\\) and a line \\(x-y+2 \sqrt {2}=0\\) are tangent.  
\\((1)\\) Find the equation of circle \\(O\\);  
\\((2)\\) A line \\(l\\) passing through the point \\((1, \dfrac { \sqrt {3}}{3})\\) intersects the circle with a chord length of \\(2 \sqrt {3}\\), find the equation of line \\(l\\).

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