
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 certain middle school organized 7th and 8th grade students to participate in a physical fitness test. Now, $10$ students' scores (unit: points) were randomly selected from each of the 7th and 8th grades for statistical analysis.  
Collected data:  
7th grade: $78$, $90$, $80$, $95$, $68$, $90$, $90$, $100$, $75$, $80$;  
8th grade: $80$, $70$, $85$, $95$, $90$, $100$, $90$, $85$, $90$, $78$.  
Organized data:  

| Score $x/$ points | $60\leqslant x\leqslant 70$ | $70 \lt x\leqslant 80$ | $80 \lt x\leqslant 90$ | $90 \lt x\leqslant 100$ |
|-------------------|---------------------------|-----------------------|-----------------------|------------------------|
| 7th grade         | $1$                       | $4$                   | $3$                   | $2$                    |
| 8th grade         | $1$                       | $2$                   | $a$                   | $b$                    |

Analyzed data:  

| Statistic       | Mean   | Median | Mode |
|-----------------|--------|--------|------|
| 7th grade       | $84.6$ | $c$    | $90$ |
| 8th grade       | $86.3$ | $87.5$ | $d$  |

$(1)$ Fill in the blanks: $a=$______, $b=$______, $c=$______, $d=$______;  
$(2)$ If there are a total of $200$ students from the 8th grade participating in the test, estimate the number of students from the 8th grade who scored above $80$ points;  
$(3)$ Based on the data above and your knowledge of statistics, which grade of students do you think has better physical fitness, and explain the reason (provide one reason is enough).

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