
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 \( x_{1} \) and \( x_{2} \) be the roots of the equation \( x^{2} + x + 1 = 0 \). Then, the value of the series \( \frac{x_{1}}{x_{2}}+\left(\frac{x_{1}}{x_{2}}\right)^{2}+\left(\frac{x_{1}}{x_{2}}\right)^{3}+\cdots+\left(\frac{x_{1}}{x_{2}}\right)^{1998} \) is equal to \(\qquad\) \(\_\_\_\_\_\).

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