
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 the terminal side of angle $\alpha$ ($0 < \alpha < \frac{\pi}{2}$) passes through the point $(\cos 2\beta, 1+\sin 3\beta \cos \beta - \cos 3\beta \sin \beta)$, where $\frac{\pi}{2} < \beta < \pi$ and $\beta \neq \frac{3\pi}{4}$, calculate $\alpha - \beta$.

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