
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
Three students are participating in a pie-eating contest. The first student eats $\frac{5}{6}$ of one pie, the second student eats $\frac{7}{8}$ of one pie, and the third student eats $\frac{1}{2}$ of one pie. How much less pie did the third student eat compared to the total amount the first two students ate together? Express your answer as a fraction of one pie, reduced to simplest form.

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