
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
When two points equally divide a unit circle, the corresponding correct relationship is $\sin \alpha + \sin (\pi + \alpha) = 0$. When three points equally divide a unit circle, the corresponding correct relationship is $\sin \alpha + \sin \left(\alpha + \frac{2\pi}{3}\right) + \sin \left(\alpha + \frac{4\pi}{3}\right) = 0$. From this, the corresponding correct relationship for four points equally dividing a unit circle can be deduced as \_\_\_\_\_\_\_.

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