
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 triangle ABC, where A, B, C are the internal angles and a, b, c are their respective opposite sides. If A = $ \frac{\pi}{6} $, b = $(4 + 2\sqrt{3})a\cos B$, and b = 1, find the value of angle B and the area of triangle ABC.

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