
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  $\lambda$  the positive root of the equation  $t^2-1998t-1=0$ .  It is defined the sequence  $x_0,x_1,x_2,\ldots,x_n,\ldots$  by  $x_0=1,\ x_{n+1}=\lfloor\lambda{x_n}\rfloor\mbox{ for }n=1,2\ldots$  Find the remainder of the division of  $x_{1998}$  by  $1998$ . 

Note:  $\lfloor{x}\rfloor$  is the greatest integer less than or equal to  $x$ .

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