
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
1. Given that $α$ and $β$ are acute angles, and $\cos α= \frac{4}{5}$, $\cos (α+β)=- \frac{16}{65}$, find the value of $\cos β$.
2. Given that $0 < β < \frac{π}{4} < α < \frac{3}{4}π$, $\cos ( \frac{π}{4}-α)= \frac{3}{5}$, $\sin ( \frac{3π}{4}+β)= \frac{5}{13}$, find the value of $\sin (α+β)$.

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