
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
Tanya and Katya made an experiment and obtained two positive real numbers, each of which was between 4 and 100 inclusive. Tanya wrote the two numbers \( x \) and \( y \) and found their average, while Katya wrote the second number twice and took the average of the three numbers \( x \), \( y \), and \( y \). What is the maximum number by which their results may differ?

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