
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 $\cos (\alpha -\frac{β}{2})=-\frac{2\sqrt{7}}{7}$, $\sin (\frac{α}{2}-\beta )=\frac{1}{2}$, and $\alpha \in (\frac{π}{2}$, $\pi )$, $\beta \in (0$, $\frac{π}{2})$. Find:<br/>$(1)\cos \frac{α+β}{2}$;<br/>$(2)\tan \left(\alpha +\beta \right)$.

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