
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
Let S<sub>n</sub> be the sum of the first n terms of the sequence {a<sub>n</sub>}, given that a<sub>1</sub>\=8, a<sub>n+1</sub>\=S<sub>n</sub>+8.
(Ⅰ) Find the general term formula for the sequence {a<sub>n</sub>}.
(Ⅱ) Find the smallest positive integer n such that the inequality a<sub>1</sub>•a<sub>2</sub>•a<sub>3</sub>…a<sub>n</sub>＞1000 holds.

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