
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
Consider the sequence of integers  $ \left( a_n\right)_{n\ge 0} $  defined as  $$  a_n=\left\{\begin{matrix}n^6-2017, & 7|n \frac{1}{7}\left( n^6-2017\right) , & 7\not | n\end{matrix}\right. .  $$  Determine the largest length a string of consecutive terms from this sequence sharing a common divisor greater than  $ 
1 $  may have.

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