
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 \\(P\\) with center at point \\(P\\), circle \\(P\\) passes through point \\(F(1,0)\\) and is tangent to the line \\(l\\): \\(x=-1\\).  
\\((\\)I\\()\\) Find the equation of the trajectory \\(C\\) of point \\(P\\);  
\\((\\)II\\()\\) If circle \\(P\\) intersects with circle \\(F\\): \\((x-1)^{2}+y^{2}=1\\) at points \\(M\\) and \\(N\\), find the range of values for \\(|MN|\\).

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