
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 $α \in \left( \frac{π}{2}, π \right)$, and $\sin α = \frac{1}{3}$.

$(1)$ Find the value of $\sin 2α$;  
$(2)$ If $\sin (α+β) = -\frac{3}{5}$, and $β \in (0, \frac{π}{2})$, find the value of $\sin β$.

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