
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 \( x_{1}, x_{2}, \cdots, x_{n} \) be a sequence of positive integers where each term is not greater than \( M \) and satisfies
\[ x_{k} = \left| x_{k-1} - x_{k-2} \right|, \quad k = 3, 4, \ldots, n. \]
How many terms can such a sequence have at most?

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