
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 that a, b, c are all nonzero complex numbers and \(\frac{a}{b} = \frac{b}{c} = \frac{c}{a}\), find the value of \(\frac{a+b-c}{a-b+c}\) (where \(w = \frac{-1+\sqrt{3} \mathrm{i}}{2}\)).

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