
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 $4$ teachers. During the first period, each student is enrolled in one class, and each teacher is teaching one class. The enrollments in the classes are $40, 30, 30, and 20$. Let $t$ be the average number of students in a class if a teacher is selected at random, and let $s$ be the average number of students in the class of a randomly picked student, including the student themselves. Compute $t-s$.

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