
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 $100$ students divided among $5$ classes taught by $5$ teachers, with each teacher teaching one class. The student distribution across the classes is $40, 40, 10, 5, 5$. Compute the value of $t-s$, where $t$ is the expected number of students per class when choosing a teacher at random and $s$ is the expected number of students per class when choosing a student at random.

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