
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
Given a sequence of positive integers \(X_{1}, X_{2}, \ldots, X_{n}\), where all elements do not exceed a certain number \(M\). It is known that for all \(k > 2\), \(X_{k} = \left|X_{k-1} - X_{k-2}\right|\). What can be the maximum length of this sequence?

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