
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
Let \( n \) be a positive integer not exceeding 1996. If there exists a \( \theta \) such that \( (\sin \theta + i \cos \theta)^{n} = \sin \theta + i \cos n \theta \), find the number of possible values for \( n \).

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