
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
Regarding the equation \(x^{3} + t x + s = 0\), where \(t \in \mathbb{R}\), \(s \in \mathbb{C}\), and \(\arg s = \frac{\pi}{6}\), it has 3 complex roots. These roots correspond to the vertices of an equilateral triangle with side length \(\sqrt{3}\) in the complex plane. Find the values of \(s\) and \(t\).

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