
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 angles $A$, $B$, and $C$ correspond to sides $a$, $b$, and $c$ respectively, and $b=2$.
(1) If $a\sin(2B)=\sqrt{3}b\sin(A)$, find $B$.
(2) If $a$, $b$, and $c$ form a geometric sequence, find the maximum area of triangle $ABC$.

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