
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
For the equation \( x^{3} + t x + s = 0 \) (where \( t \in \mathbf{R}, s \in \mathbf{C}, \arg s = \frac{\pi}{6} \)) that has 3 complex roots, the corresponding points on the complex plane form the vertices of an equilateral triangle with side length \( \sqrt{3} \). Find the values of \( s \) and \( t \).

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