
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 at more than $\textdollar 120$. There are three coupons available: Coupon A gives $18\%$ off the listed price, Coupon B gives $\textdollar 35$ off the listed price, and Coupon C gives $20\%$ off the amount by which the listed price exceeds $\textdollar 120$. Let $x$ and $y$ be the smallest and largest prices, respectively, for which Coupon A saves at least as many dollars as Coupon B or C. Determine $y-x$.
A) 905.56
B) 1005.56
C) 1105.56
D) 1205.56

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