
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 \( z_0 + z_1 + z_2 + \cdots \) be an infinite complex geometric series such that \( z_0 = 1 \) and \( z_{2013} = \frac{1}{2013^{2013}} \). Find the sum of all possible sums of this series.

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