
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 $A$, $B$, and $C$ and their respective opposite sides $a$, $b$, and $c$. $B$ is an obtuse angle, and $\sqrt{3}a = 2b\sin A$.

1. Find the measure of angle $B$.
2. If the area of $\triangle ABC$ is $\frac{15\sqrt{3}}{4}$ and $b=7$, find the value of $a+c$.
3. If $b=6$, find the maximum area of $\triangle ABC$.

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