
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 is attending one class, and each teacher is conducting one class. The enrollments in the classes are \( 40, 30, 20, 10, 10, \) and \( 10 \). Let \( t \) be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let \( s \) be the average value obtained if a student was picked at random and the number of students in their class, including the student, is noted. What is \( t-s \)?
A) \(-8.33\)
B) \(-6.67\)
C) \(0\)
D) \(6.67\)
E) \(8.33\)

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