
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
If $α$ and $β$ belong to $\left(0, \frac{π}{2}\right)$, and $\sin \left( \frac{α}{2}-β\right)=- \frac{1}{2}$, $\cos \left(α- \frac{β}{2}\right)= \frac{\sqrt{3}}{2}$, then $α+β=$ ______.

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