
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
Lily and John shared a pizza with $12$ equally-sized slices. Lily wanted a plain pizza, but John wanted pepperoni on one-third of the pizza. The cost of a plain pizza was $12$ dollars, and adding pepperoni to one-third of the pizza cost an additional $3$ dollars. John ate all the pepperoni slices and two plain slices. Lily ate the remaining slices. Each paid for what they had eaten. Calculate the difference in the amount of money paid by John and Lily.

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