
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 120 students and 6 teachers, with enrollments in the classes being 60, 30, 10, 10, 5, and 5, find the difference between the average number of students in a teacher's class and the average number of students in a class, including the student who is picked at random.

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