
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 acute triangle \\(\triangle ABC\\), the sides opposite angles \\(A\\), \\(B\\), and \\(C\\) are \\(a\\), \\(b\\), and \\(c\\) respectively. The vectors \\( \overrightarrow{m}=(2\sin (A+C),- \sqrt {3})\\) and \\( \overrightarrow{n}=(1-2\cos ^{2} \frac {B}{2},\cos 2B)\\) are given, and \\( \overrightarrow{m} \perp \overrightarrow{n}\\).  
\\((1)\\) Find the magnitude of angle \\(B\\);  
\\((2)\\) If \\(\sin A\sin C=\sin ^{2}B\\), find the value of \\(a-c\\).

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