
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
The sequence $\{a_n\}$ is a permutation of the numbers 1, 2, 3, ..., 2016. Define set B as $B=\{x | x= \sum_{i=1}^{m}a_{n+i}, n=0, 1, 2, \ldots, 2016-m\}$.
(Ⅰ) If $m=8$, determine the maximum value of the elements in set B.
(Ⅱ) In the following cases, is it possible for set B to be a singleton set? If so, provide an example of sequence $\{a_n\}$. If not, explain why not.
  ① $m=8$, $n=8k$, $k=0,1,2,\ldots,251$;
  ② $m=3$, $n=3k$, $k=0,1,2,\ldots,671$.
(Ⅲ) For sequence $\{a_n\}$ and $m=8$, let the maximum value of the red elements in B be D. Find the minimum value of S.

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