
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
Determine all sequences of non-negative integers  $a_1, \ldots, a_{2016}$  all less than or equal to  $2016$  satisfying  $i+j\mid ia_i+ja_j$  for all  $i, j\in \{ 1,2,\ldots, 2016\}$ .

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