
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 smallest positive integer \( n \) such that there exists a sequence of \( n+1 \) terms \( a_0, a_1, \ldots, a_n \) with the properties \( a_0 = 0 \), \( a_n = 2008 \), and \( |a_i - a_{i-1}| = i^2 \) for \( i = 1, 2, \ldots, n \).

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