
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
We call a 5-tuple of integers arrangeable if its elements can be labeled \(a, b, c, d, e\) in some order so that \(a - b + c - d + e = 29\). Determine all 2017-tuples of integers \(n_1, n_2, \ldots, n_{2017}\) such that if we place them in a circle in clockwise order, then any 5-tuple of numbers in consecutive positions on the circle is arrangeable.

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