
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 interior angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, it is known that $B=60^\circ$, and $c=8$.  
(1) If point $M$ is the midpoint of segment $BC$, and $\frac{AM}{BM}= \sqrt{3}$, find the value of $b$;  
(2) If $b=12$, find the area of $\triangle ABC$.

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