
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 \( \alpha \in \mathbf{R} \), if the set \( \{\sin \alpha, \cos 2\alpha\} = \{\cos \alpha, \sin 2\alpha\} \), then the set of all angles \( \alpha \) that satisfy the requirement is \(\qquad\) .

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