
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
What is the maximum possible length of a sequence of natural numbers \( x_1, x_2, x_3, \ldots \) such that \( x_i \leq 1998 \) for \( i \geq 1 \), and \( x_i = |x_{i-1} - x_{i-2} | \) for \( i \geq 3 \)?

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