
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. It is given that \\(a^{2}-c^{2}=2b\\) and \\(\sin A\cos C=3\cos A\sin C\\).  
\\((1)\\) Find the value of \\(b\\);  
\\((2)\\) If \\(B= \dfrac {\pi}{4}\\), and \\(S\\) is the area of \\(\triangle ABC\\), find the range of values for \\(S+8 \sqrt {2}\cos A\cos C\\).

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