
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 shop offers a special discount on items priced above $\textdollar120$. There are three different discount options available. Coupon X offers 20% off the total list price. Coupon Y deducts $\textdollar40$ from the list price. Coupon Z provides a 30% discount on the portion of the list price that exceeds $\textdollar120$. Let $x$ and $y$ represent the smallest and largest list prices for which Coupon X provides at least as much savings as either Coupon Y or Z. What is $y - x$?
A) 140
B) 150
C) 160
D) 170
E) 180

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