
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are denoted as $a$, $b$, $c$, respectively, with $C= \frac{\pi}{3}$, $b=8$, and the area of $\triangle ABC$ is $10\sqrt{3}$.

(Ⅰ) Find the value of $c$;

(Ⅱ) Find the value of $\cos(B-C)$.

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