
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 $\triangle ABC$ have sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively, and $a=8$, $A=\frac{π}{3}$.  
$(1)$ If $B≠\frac{π}{2}$, find the value of $\frac{{2c-b}}{{\cos B}}$;  
$(2)$ Find the minimum value of $|{\overrightarrow{AB}+\overrightarrow{AC}}|-\overrightarrow{AB}•\overrightarrow{AC}$.

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