
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 polar coordinate system, it is known that the center of circle \\(C\\) is \\(C(\sqrt{2}, \frac{\pi}{4})\\), and the radius \\(r=\sqrt{3}\\).

    \\((1)\\) Find the polar equation of circle \\(C\\);

    \\((2)\\) If \\(\alpha \in [0, \frac{\pi}{4}]\\), the parametric equation of line \\(l\\) is \\(\begin{cases} x=2+t\cos \alpha \\ y=2+t\sin \alpha \end{cases}\\) (\\(t\\) is the parameter), and line \\(l\\) intersects circle \\(C\\) at points \\(A\\) and \\(B\\), find the range of the chord length \\(|AB|\\).

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