
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 two points in the plane, \\(A(4,0)\\) and \\(B(0,2)\\):  
\\((1)\\) Find the equation of the line \\(l\\) that passes through point \\(P(2,3)\\) and is parallel to line \\(AB\\);  
\\((2)\\) Let \\(O(0,0)\\), find the equation of the circumscribed circle of \\(\triangle OAB\\).

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