
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
\( k \) is the positive root of the equation \( x^2 - 1998x - 1 = 0 \). Define the sequence \( x_0, x_1, x_2, \ldots \) by \( x_0 = 1 \) and \( x_{n+1} = \lfloor k x_n \rfloor \). Find the remainder when \( x_{1998} \) is divided by 1998.

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