
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 that \\(\Delta ABC\\) is an acute triangle, with vectors \\(\vec{m}=\left( \cos\left( A+\frac{\pi}{3} \right), \sin\left( A+\frac{\pi}{3} \right) \right)\\), \\(\vec{n}=\left( \cos B, \sin B \right)\\) and \\(\vec{m} \perp \vec{n}\\).

\\((1)\\) Find the value of \\(A-B\\);

\\((2)\\) If \\(\cos B=\frac{3}{5}\\) and \\(AC=8\\), find the length of \\(BC\\).

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