
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 $\triangle ABC$, let $a$, $b$, and $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively. Given that $\sqrt{3}b\sin A - a\cos B = 2a$.

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

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