
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
A retailer offers three different discount sequences on a product. Which of the following single percentage discounts would always be greater than any of the following discount sequences for the consumer:
(1) a $20\%$ discount followed by a $10\%$ discount
(2) three successive $8\%$ discounts
(3) a $15\%$ discount followed by a $12\%$ discount
Determine the smallest possible positive integer value of $n\%$ that is greater than any of these discount sequences.
A) 27
B) 28
C) 29
D) 30
E) 31

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