
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 moving circle \\(C\\) that passes through a fixed point \\(F(0,1)\\) and is tangent to the line \\(l_{1}\\): \\(y=-1\\), the trajectory of the center \\(C\\) is \\(E\\).

  

\\((1)\\) Find the equation of the trajectory of the moving point \\(C\\);

  

\\((2)\\) It is known that the line \\(l_{2}\\) intersects the trajectory \\(E\\) at two points \\(P\\) and \\(Q\\), and the ordinate of the midpoint of \\(PQ\\) is \\(2\\). What is the maximum value of \\(|PQ|\\)?

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