
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 acute triangle \\(\Delta ABC\\), the sides opposite to angles \\(A, B, C\\) are respectively \\(a, b, c\\). Given \\(\overrightarrow{m} = (\sqrt{3}a, c)\\), \\(\overrightarrow{n} = (\sin A, \cos C)\\), and \\(\overrightarrow{m} = 3\overrightarrow{n}\\).

\\((1)\\) Find \\(C\\).

\\((2)\\) Find the range of the perimeter of \\(\Delta ABC\\).

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