
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 $v_n$ be the $n^\text{th}$ term of the sequence
\[ 1, \,\, 4, \,\, 7, \,\, 10, \,\, 13, \,\, 16, \,\, 19, \,\, 22, \,\, 25, \,\, 28, \ldots, \]
where the first term is 1, and each group of terms in the sequence increases by two more terms than the previous group and each term within a group increases by 3 from the previous term. The groups are structured as follows:
\[\underbrace{1}_{1\text{ term}}, \,\, \underbrace{4, \, 7, \, 10}_{3\text{ terms}}, \,\, \underbrace{13, \, 16, \, 19, \, 22, \, 25}_{5\text{ terms}}, \,\, \underbrace{28, \ldots}_{7\text{ terms}}, \ldots.\]
Determine $v_{2008}$.

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