
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 and Bob shared a pizza with $12$ equally-sized slices. Alice likes a plain pizza, while Bob prefers mushrooms on only one-third of the pizza. The cost of a plain pizza was $12$ dollars, and there was an additional cost of $3$ dollars for putting mushrooms on one-third of the pizza. Bob ate all the mushroom-topped slices and three plain slices. Alice ate the remainder. Each paid for what they had eaten. What is the amount of money that Bob paid more than Alice?

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