
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 integers $\left(a_{i}\right)_{1 \leqslant i \leqslant 2016}$ such that $0 \leqslant a_{i} \leqslant 2016$ for all $i$, and for all $i, j$, $i + j$ divides $i a_{i} + j a_{j}$.

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