
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 fire department of a city decided to conduct a simple random sampling survey of fire safety in households to understand the fire safety situation of the residents. Fifteen residents were randomly selected from both the urban and suburban areas for a test on fire safety knowledge (with a maximum score of 100). Data collected: Urban residents: $81$, $95$, $83$, $77$, $83$, $80$, $81$, $70$, $81$, $73$, $78$, $82$, $80$, $70$, $50; Suburban residents: $74$, $81$, $75$, $76$, $70$, $75$, $75$, $79$, $81$, $70$, $74$, $80$, $91$, $45$, $82. Organize data:

|              | $x < 60$ | $60 \leq x < 80$ | $80 \leq x < 90$ | $90 \leq x \leq 100$ |
|--------------|-----------|------------------|------------------|----------------------|
| Urban residents (people) | $1$ | $5$ | $8$ | $1$ |
| Suburban residents (people) | $1$ | $a$ | $4$ | $1$ |

Analyze data:

|              | Mean | Mode | Median | Variance |
|--------------|------|------|--------|----------|
| Urban residents | $77.6$ | $b$ | $80$ | $88.37$ |
| Suburban residents | $75.2$ | $75$ | $c$ | $91.36$ |

Based on the above data, solve the following problems:

$(1)$ Directly write $a=$______, $b=$______, $c=$______;

$(2)$ According to the above data, it can be inferred that ______ residents perform better (fill in "Urban" or "Suburban");

$(3)$ If $1000$ residents are randomly selected from the urban area of the city to participate in the test of fire safety knowledge, it is estimated that about ______ residents will have excellent scores (scores not less than $80$).

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