
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 that $α$ and $β ∈ (0, \frac{π}{2})$, $\frac{\tan \frac{α}{2}}{1 - \tan^{2} \frac{α}{2}} = \frac{\sqrt{3}}{2}$, and $2\sin β = \sin(α + β)$, find the value of $β$.

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