
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 store offers an item priced above $\textdollar 120$. A shopper can use one of three coupons on their purchase. Coupon A gives $20\%$ off the total price, Coupon B provides a flat discount of $\textdollar 40$, and Coupon C offers a $30\%$ discount off the amount exceeding $\textdollar 120$. Determine the highest and lowest prices, labeled $y$ and $x$ respectively, for which Coupon A saves at least as much as either Coupon B or Coupon C. What is $y - x$?
A) 120
B) 140
C) 160
D) 180
E) 200

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