
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
Find the number of sequences \(a_{1}, a_{2}, \ldots, a_{10}\) of positive integers with the property that \(a_{n+2} = a_{n+1} + a_{n}\) for \(n = 1, 2, \ldots, 8\), and \(a_{10} = 2002\).

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