
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 $\alpha$ and $\beta$ satisfy $0 < \alpha < 2\beta \leq \frac{\pi}{2}$, and $2\cos(\alpha+\beta)\cos\beta = -1 + 2\sin(\alpha+\beta)\sin\beta$, the relationship between angle $\alpha$ and angle $\beta$ is \_\_\_\_\_\_.

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