
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 an acute triangle $ABC$, where $a, b, c$ represent the sides opposite to angles $A, B, C$ respectively, it is given that $a = 2b\sin A$.
1. Find the size of $\angle B$.
2. If $a = 3\sqrt{3}$ and $c = 5$, find the area of triangle $ABC$ and the value of $b$.

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