
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 that in acute triangle ABC, the sides opposite to angles A, B, C are a, b, c respectively, and bsinA = acos(B - $ \frac{\pi}{6}$).
(1) Find the value of angle B.
(2) If b = $\sqrt{13}$, a = 4, and D is a point on AC such that S<sub>△ABD</sub> = 2$\sqrt{3}$, find the length of AD.

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