
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 school with 200 students and 5 teachers, the enrollment numbers for the classes are 80, 60, 40, 15, and 5. If a teacher is picked at random and the number of students in their class is noted, calculate the average value obtained. If a student was picked at random and the number of students in their class, including the student, is noted, calculate the average value obtained, and find the difference between the two averages.

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