
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 \(\lambda\) be the positive root of the equation \(t^{2}-1998t-1=0\). Let \((x_{n})\) be a sequence defined by \(x_{0}=1\) and, for all \(n \geqslant 0\),

\[ x_{n+1}=[\lambda x_{n}] \]

where \([x]\) denotes the integer part of \(x\). Calculate the remainder of the Euclidean division of \(x_{1998}\) by 1998.

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