
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 \frac{α}{2}+ \cos \frac{α}{2} = \frac{\sqrt{6}}{2}$.
1. Find the value of $\tan\left(α+ \frac{π}{4}\right)$;
2. If $\sin(α-β)=-\frac{3}{5}$, with $β \in \left(\frac{π}{2}, π\right)$, find the value of $\cos β$.

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