
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
Valerie, Tim, and Priya went on a camping trip and decided to split all the costs equally. During their trip, each incurred certain expenses: Valerie paid X dollars, Tim paid Y dollars, and Priya paid Z dollars, where \( X < Y \) and \( X < Z \). Determine how much extra money must Valerie give to Priya to ensure each has shared costs equally.
A) $\frac{X+Y-2Z}{3}$
B) $\frac{Y-Z}{2}$
C) $\frac{Z-X}{2}$
D) $\frac{Y+Z-2X}{3}$

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