
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
Let the sequences \(\left\{x_{n}\right\}\) and \(\left\{y_{n}\right\}\) satisfy \( x_{n} + i y_{n} = \left(\frac{\sqrt{3}i - 1}{2}\right)^{n} \). Find the sum of the first 1994 terms of the sequence \(\left\{x_{n}\right\}\), denoted by \(S_{1994}\).

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