
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 shopper considers buying an item priced over $200 and can use one of three coupons for discounts. Coupon A provides a 20% discount on the listed price, Coupon B offers a $50 reduction, and Coupon C grants a 30% discount on the amount exceeding $200. Determine the price range [x, y] where Coupon A results in savings equal to or greater than those from Coupons B and C. What is the value of y - x?
A) 100
B) 200
C) 300
D) 350
E) 400

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