
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
The sequence \(\left\{\alpha_{n}\right\}\) is an arithmetic sequence with common difference \(\beta\). The sequence \(\left\{\sin \alpha_{n}\right\}\) is a geometric sequence with common ratio \(q\). Given \(\alpha_{1}\) and \(\beta\) are real numbers, find \(q\).

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