
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 in \\(\triangle ABC\\), the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are respectively \\(a\\), \\(b\\), and \\(c\\).

    \\((1)\\) If the lengths of sides \\(a\\), \\(b\\), \\(c\\) form an arithmetic sequence in order, and \\(\sin A : \sin B = 3 : 5\\), find the degree of the largest angle among the three internal angles;

    \\((2)\\) If \\(\overrightarrow{BA} \cdot \overrightarrow{BC} = b^2 - (a - c)^2\\), find \\(\cos B\\).

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