
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 the equation \( x^{4} + \frac{1}{3} \sin \alpha \cdot x^{2} + \frac{1}{200} \cos \frac{\pi}{3} = 0 \), where the four roots form an arithmetic sequence and \(\alpha\) is between \(0\) and \(2\pi\), find the value of angle \(\alpha\) and the values of the four roots.

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