
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
A sequence of natural numbers \( a_{0}, a_{1}, a_{2}, a_{3}, \ldots \) is formed according to the following rule:

\[
a_{0}, a_{1}, a_{2} = \left|a_{0} - a_{1}\right|, a_{3} = \left|a_{1} - a_{2}\right|, \ldots
\]

(in general, \( a_{n} = \left|a_{n-2} - a_{n-1}\right| \) for all \( n \geq 2 \)); the sequence continues until the first zero appears. It is known that each number in the sequence does not exceed 1967. What is the maximum number of terms this sequence can contain?

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