
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 $a$, $b$, $c$ respectively. Given that $C=\frac{2\pi}{3}$ and $a^2 - (b-c)^2 = (2-\sqrt{3})bc$.

1. Find the measure of angle $B$.
2. If the common difference of the arithmetic sequence ${a_n}$ is not zero, and $a_1 \cdot \cos 2B = 1$, and $a_2, a_4, a_8$ form a geometric sequence, find the sum of the first $n$ terms of the sequence $\left\{\frac{4}{a_n a_{n+1}}\right\}$, denoted as $S_n$.

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