
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
In a test, each question has five answer choices. A top student answers all questions correctly. A failing student answers correctly when they manage to cheat, and otherwise answers randomly (i.e., answers correctly on $1 / 5$ of the questions they did not cheat on). Overall, the failing student answered half of the questions correctly. What fraction of the answers did they manage to cheat on?

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