
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
A pizza with $12$ equally-sized slices costs $12$ dollars. A topping of olives on a quarter of the pizza adds an additional cost of $3$ dollars, whereas a topping of mushrooms on half of the pizza adds an additional $4$ dollars. Dave ate all the slices with mushrooms and two slices with olives, while Doug ate the remaining slices. Determine the difference in the amount Dave paid and the amount Doug paid.

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