
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
Alice, Bob, and Charlie shared a pizza with 12 equally-sized slices. Alice wanted a plain pizza, but Bob wanted pepperoni on one-third of the pizza, and Charlie wanted mushrooms on a different one-third of the pizza. The cost of a plain pizza was $12$ dollars, and there was an additional cost of $3$ dollars for pepperoni and $2$ dollars for mushrooms on their respective thirds. Bob ate all the pepperoni slices and two plain slices. Charlie ate all the mushroom slices and one plain slice. Alice ate the remainder. Each paid for what they had eaten. What is the difference in the amount Bob paid and the amount Alice paid?

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