
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
Let $\triangle ABC$ be an acute-angled triangle, with the sides opposite angles $A$, $B$, $C$ denoted as $a$, $b$, $c$ respectively, and it is given that $(\sin A-\sin B)(\sin A+\sin B)=\sin \left( \frac {\pi}{3}-B\right)\sin \left( \frac {\pi}{3}+B\right)$.  
(I) Find the value of angle $A$;  
(II) If $\overrightarrow{AB} \cdot \overrightarrow{AC}=12$ and $a=2\sqrt{7}$, find $b$ and $c$ (where $b < c$).

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