
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 triangle \\(ABC\\), the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are denoted as \\(a\\), \\(b\\), and \\(c\\) respectively. Given vectors \\( \overrightarrow{m}=(\cos B,2\cos ^{2} \frac {C}{2}-1)\\) and \\( \overrightarrow{n}=(c,b-2a)\\), and \\( \overrightarrow{m}\cdot \overrightarrow{n}=0\\).  
\\((1)\\) Find the magnitude of angle \\(C\\);  
\\((2)\\) If the area of \\(\triangle ABC\\) is \\(2 \sqrt {3}\\) and \\(a+b=6\\), find \\(c\\).

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