
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
Aman, Bella, and Charlie went on a holiday trip and agreed to share the costs equally. During the holiday, they took turns paying for shared expenses like meals and accommodations. At the end of the trip, Aman had paid $X$ dollars, Bella had paid $Y$ dollars, and Charlie had paid $Z$ dollars, where $X < Y < Z$. How many dollars must Aman give to Charlie so that they all share the costs equally?

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