
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 three coupons for purchasing items priced above $\textdollar 200$. Coupon A provides a $20\%$ discount off the listed price, Coupon B offers a $\textdollar 50$ flat discount on the price, and Coupon C provides a $30\%$ discount off the amount exceeding $\textdollar 200$. Determine the largest ($y$) and smallest ($x$) prices for which the savings from Coupon A equal or exceed the savings provided by both Coupons B and C. Calculate the value of $y - x$.
A) 250
B) 300
C) 350
D) 400
E) 450

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