
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
Doug and Dave shared a pizza with 8 equally-sized slices. Doug wanted a plain pizza, but Dave wanted not only anchovies on half the pizza but also mushrooms on a different quarter. The cost of a plain pizza was $8$ dollars, anchovies added an extra $2$ dollars to half the pizza, and mushrooms added an extra $1$ dollar to a quarter of the pizza. Dave ate all the slices with anchovies, all the slices with mushrooms, and one plain slice. Doug ate the remainder. Each paid for what he had eaten. What is the difference in dollars between the total cost of what Dave paid and the total cost of what Doug paid?

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