
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
In a certain area, the principle of "green travel" is promoted through the operation of "shared bicycles." An interest group in a senior high school in the area consists of 20 senior two students and 15 senior one students. Now, using stratified sampling, 7 people are selected to form an experiential group to experience the use of "shared bicycles" in the market. The questions are:<br/>
$(1)$ How many senior one and senior two students should be selected from this interest group?<br/>
$(2)$ Given that there are two models of "shared bicycles," $X$ and $Y$, in the area, in the market experience, the senior two students in the experiential group rent model $X$ bicycles, and the senior one students rent model $Y$ bicycles.<br/>
① If 3 people are randomly selected from the group, find the probability that at least 2 of the 3 people rented model $X$ bicycles during the market experience.<br/>
② Given that the rental fee for model $X$ bicycles is 1 yuan per hour and for model $Y$ bicycles is 1.2 yuan per hour, let $Z$ be the sum of the hourly rental fees obtained by randomly selecting 3 people from the experiential group. Find the distribution table and mathematical expectation of $Z$.

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