
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
Given the listed price of an item is greater than $\textdollar 150$, and the shopper can use one of three coupons: Coupon A offers 15% off the listed price, Coupon B provides a $\textdollar 30$ flat discount, and Coupon C offers 20% off the amount by which the listed price exceeds $\textdollar 150$, determine the difference between the smallest and largest prices for which Coupon A saves more dollars than both Coupon B and Coupon C.

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