
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
In the Cartesian coordinate system, with the origin \\(O\\) as the pole and the non-negative half-axis of the \\(x\\)-axis as the polar axis, a polar coordinate system is established. It is known that the polar coordinates of point \\(M\\) are \\((2 \sqrt{2}, \frac{\pi}{4})\\), and the parametric equation of curve \\(C\\) is \\(\begin{cases}x=1+2\cos \alpha \\ y=2\sin \alpha\end{cases} (\alpha\\) is the parameter\\()\\).
\\((1)\\) Line \\(l\\) passes through \\(M\\) and is tangent to curve \\(C\\). Find the polar equation of line \\(l\\).
\\((2)\\) Point \\(N\\) is symmetric to point \\(M\\) with respect to the \\(y\\)-axis. Find the range of distances from points on curve \\(C\\) to point \\(N\\).

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