
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 $ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$, such that $\sin(2A + B) = 2\sin A + 2\cos(A + B)\sin A$.

1. Find the value of $\frac{a}{b}$.
2. If the area of triangle $ABC$ is $\frac{\sqrt{3}}{2}$ and $a = 1$, find the value of $c$.

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