
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, and it is given that \\(b\cos C = 3a\cos B - c\cos B\\).

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

\\((2)\\) If \\(\overrightarrow{BA} \cdot \overrightarrow{BC} = 2\\) and \\(b = 2\sqrt{2}\\), find the values of \\(a\\) and \\(c\\).

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