
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 customer is comparing a single discount of $n\%$ with these discount options on the initial price of an item:
(1) A $20\%$ discount followed by a $10\%$ discount.
(2) Two successive $18\%$ discounts.
(3) Three successive $12\%$ discounts.
Find the minimum integer value of $n$ for which the single discount $n\%$ is more advantageous than any of the described options.
A) 30
B) 31
C) 32
D) 33
E) 34

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