
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, only $4$ teachers are teaching, with class enrollments being $60, 30, 20,$ and $10$. In the second period, all $6$ teachers teach, with class enrollments of $40, 30, 20, 10, 10,$ and $10$. Let $t_1$ be the average number of students per class in the first period and $t_2$ be the average in the second period. Let $s$ be the average number of students per student as noted in the first period classes. Calculate $t_1 - s$ and $t_2 - s$.
A) $-21.66, -11.66$
B) $-11.66, -21.66$
C) $11.66, 21.66$
D) $21.66, 11.66$

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