
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 \(\{a_n\} (n \geq 0)\) that satisfies \(a_0 = 0\), \(a_1 = 1\), and for all positive integers \(n\), \(a_{n+1} = 2a_n + 2007a_{n-1}\), find the smallest positive integer \(n\) such that \(2008\) divides \(a_n\).

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