
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
Tom and Jerry went on a camping trip and agreed to split all expenses equally. During the trip, Tom paid $x$ dollars, while Jerry paid $y$ dollars. Given that $x > y$, calculate how much money should Jerry give to Tom to ensure both spent equally.
A) $\frac{x + y}{2}$   
B) $\frac{y - x}{2}$   
C) $\frac{x - y}{2}$   
D) $\frac{x - y}{4}$   
E) $x + y$

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