
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 $α,β∈(0, \dfrac{π}{2})$ and $\sin(α+2β)=\dfrac{1}{3}$.  
(1) If $α+β=\dfrac{2π}{3}$, find the value of $\sin β$;  
(2) If $\sin β=\dfrac{4}{5}$, find the value of $\cos α$.

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