
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 \\(a\\), \\(b\\), and \\(c\\) respectively. Given vectors \\(m=(\cos B,\cos C)\\) and \\(n=(4a-b,c)\\), and \\(m\parallel n\\).

\\((1)\\) Find the value of \\(\cos C\\);

\\((2)\\) If \\(c=\sqrt{3}\\) and the area of \\(\triangle ABC\\), \\(S=\frac{\sqrt{15}}{4}\\), find the values of \\(a\\) and \\(b\\).

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