
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
A school has 120 students and 6 teachers. In the first period, each student takes one class, and each teacher teaches one class. The enrollments in the classes are 40, 30, 30, 10, 5, and 5. Calculate \(t-s\) where \(t\) is the average number of students per teacher (picked at random) and \(s\) is the average number of students per student (picked at random, counting the students in their class).

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