
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 geometric sequence {z<sub>n</sub>}, where z<sub>1</sub> = 1, z<sub>2</sub> = x + yi, z<sub>3</sub> = -x + yi (where i is the imaginary unit, x, y ∈ R, and y > 0), find the sum of the first 2019 terms of the sequence {z<sub>n</sub>}.

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