
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 angles $α$ and $β$ satisfy $0 < α < 2β \leqslant \dfrac {π}{2}$, and $2\cos (α+β)\cos β=-1+2\sin (α+β)\sin β$, then the relationship between angle $α$ and angle $β$ is ______.

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