
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 $α∈\left(\frac{π}{2},π\right)$, and $\sin\frac{α}{2}+\cos\frac{α}{2}=\frac{\sqrt{6}}{2}$.

(1) Find the value of $\cos α$;
(2) If $\sin\left(α-β\right)=-\frac{3}{5}$, $β∈\left(\frac{π}{2},π\right)$, find the value of $\cos β$.

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