
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
An academy has $200$ students and $8$ teachers. The class sizes are as follows: $80, 40, 40, 20, 10, 5, 3, 2$. Calculate the average number of students per class as seen by a randomly picked teacher, represented by $t$, and the average number of students per class from the perspective of a randomly selected student, denoted as $s$, and compute the value of $t-s$.

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