
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
\[1,\,\,\, 6,\,\,\, 11,\,\,\, 16,\,\,\, 21,\,\,\, 26,\,\,\, 31,\,\,\, 36,\,\,\, 41,\,\,\, 46,\ldots,\]
where the first term is the smallest positive integer that is $1$ more than a multiple of 5, the next two terms are the next two smallest integers that are each $2$ more than a multiple of 5, the next three terms are the next three smallest integers that are each $3$ more than a multiple of 5, and so on:
\[\underbrace{1}_{1\text{ term}},\,\,\,\,\,\, \underbrace{6,\,\,\, 11}_{2\text{ terms}},\,\,\,\,\,\, \underbrace{16,\,\,\, 21,\,\,\, 26}_{3\text{ terms}},\,\,\,\,\,\, \underbrace{31,\,\,\, 36,\,\,\, 41,\,\,\, 46}_{4\text{ terms}},\,\,\,\,\,\, \underbrace{51,\ldots}_{5\text{ terms}},\,\,\,\,\,\, \ldots.\]
Determine $v_{1010}$.

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