
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
LeRoy and Bernardo went on a week-long trip and agreed to split some of their expenses based on the ratio of the amounts they could afford. Bernardo agreed to pay twice as much as LeRoy for shared dinners because he earned more. During the trip, they had three dinners costing $120, $150, and $180 respectively. If the total trip expense was split according to their agreement and it turned out LeRoy spent $A$ dollars and Bernardo spent $B$ dollars where $A < B$, how much more does LeRoy need to give Bernardo to ensure the split adjusts fairly according to their initial dinner agreement?
A) $\frac{B-A}{2} + 75$
B) $\frac{B-A}{2} - 75$
C) $\frac{A-B}{2} + 75$
D) $\frac{A+B}{2} - 75$
E) $\frac{B-A}{2} + 225$

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