
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 triangle \\(ABC\\) with sides \\(a\\), \\(b\\), and \\(c\\) opposite to angles \\(A\\), \\(B\\), and \\(C\\) respectively, and it satisfies \\(2\cos C(a\cos B+b\cos A)=c\\).
\\(①\\) Find \\(C\\);      
\\(②\\) If \\(c= \sqrt {7}\\) and \\(ab=6\\).  
Find the perimeter of \\(\triangle ABC\\).

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