
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 imaginary number \( z \) satisfies \( z^3 + 1 = 0 \), \( z \neq -1 \). Then \( \left( \frac{z}{z-1} \right)^{2018} + \left( \frac{1}{z-1} \right)^{2018} = \) .

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