
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 $\triangle ABC$ is an acute-angled triangle, vector $m=(\cos (A+\frac{\pi}{3}),\sin (A+\frac{\pi}{3}))$, $n=(\cos B,\sin B)$, and $m\perp n$.

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

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

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