
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  $n_1, n_2, . . . , n_{2017}$  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.

*Warut Suksompong, Thailand*

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