
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 a triangle $\triangle ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$, such that $b^2 + c^2 - a^2 = \sqrt{3}bc$.

(1) If $\tan B = \frac{\sqrt{6}}{12}$, find $\frac{b}{a}$;

(2) If $B = \frac{2\pi}{3}$ and $b = 2\sqrt{3}$, find the length of the median on side $BC$.

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