
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 taking one class, and each teacher is teaching one class. The enrollments in the classes are $40, 30, 30, 10, 5, 5$. Calculate the value of $t-s$, where $t$ is the average value obtained if a teacher is picked at random and the number of students in their class is noted, and $s$ is the average value obtained if a student was picked at random and the number of students in their class, including the student, is noted.

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