
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 with center \\(C\\) passing through three points \\(O(0,0)\\), \\(A(-2,4)\\), and \\(B(1,1)\\):
\\((1)\\) Find the equation of circle \\(C\\);
\\((2)\\) If the slope of line \\(l\\) is \\(- \dfrac {4}{3}\\), and the chord intercepted by circle \\(C\\) on line \\(l\\) has a length of \\(4\\), find the equation of line \\(l\\).

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