
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
Given a pizza with 12 equally-sized slices, Emily and Liam ordered a plain pizza that cost $12. Liam added mushrooms to one third of the pizza for an additional $3, and olives on another third for an additional $4. Determine the difference in the amounts Liam and Emily paid.

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