
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
The epidemic prevention and control department of a city decided to conduct a simple random sampling survey of households in the city to understand the epidemic prevention and control situation of the residents.  
Data collection:  
The staff of the epidemic prevention and control department of the city randomly selected $15$ residents from the suburban and urban areas respectively and distributed survey questionnaires to test their awareness and common knowledge of epidemic prevention and control. The test scores (in percentage) are as follows:  
Suburban residents: $74\ \ 81\ \ 75\ \ 76\ \ 70\ \ 75\ \ 75\ \ 79\ \ 81\ \ 70\ \ 74\ \ 80\ \ 91\ \ 69\ \ 82$  
Urban residents: $81\ \ 94\ \ 83\ \ 77\ \ 83\ \ 80\ \ 81\ \ 70\ \ 81\ \ 73\ \ 78\ \ 82\ \ 80\ \ 70\ \ 50$  
Data organization:  

|              | $x < 60$ | $60\leqslant x < 80$ | $80\leqslant x < 90$ | $90\leqslant x\leqslant 100$ |
|--------------|----------|----------------------|----------------------|-----------------------------|
| Suburban     | $0$      | $10$                 | $4$                  | $1$                         |
| Urban        | $1$      | $a$                  | $8$                  | $1$                         |

Explanation: Excellent for scores not less than $90$; Good for scores between $80$ and $90$; Pass for scores between $60$ and $80$ (including $60$ but not including $80$); Fail for scores below $60$.  
Data analysis:  

|              | Mean   | Median | Mode |
|--------------|--------|--------|------|
| Suburban     | $76.8$ | $b$    | $75$ |
| Urban        | $77.5$ | $80$   | $c$  |

Conclusions:  
$(1)$ Sample selection: The most reasonable method for selecting samples is to randomly select households based on the entire city's permanent residents.  
$(2)$ $a=$______,$b=$______,$c=$______;  
$(3)$ Which group of residents do you think have higher scores in the epidemic prevention and control awareness and common knowledge test? Please explain the reason;  
$(4)$ If there are a total of $15000$ suburban residents in the city, estimate the number of suburban residents with excellent scores in the epidemic prevention and control awareness and common knowledge test.

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