
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]

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[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

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In a certain middle school, there are 180 students in both the eighth and ninth grades. To understand the physical health of students in these two grades, a sampling survey was conducted as follows:
$(1)$ Data Collection:
Twenty students were randomly selected from each of the eighth and ninth grades for physical health tests. The test scores (in percentage) are as follows:

| Grade | Scores |
|-------|--------|
| Eighth | 78, 86, 74, 81, 75, 76, 87, 70, 75, 90, 75, 79, 81, 76, 74, 80, 86, 69, 83, 77 |
| Ninth | 93, 73, 88, 81, 72, 81, 94, 83, 77, 83, 80, 81, 70, 81, 73, 78, 82, 80, 70, 40 |

$(2)$ Data Organization and Description:
Organize and describe the two sets of sample data into the following score ranges:

| Score $x$ | $40\leqslant x\leqslant 49$ | $50\leqslant x\leqslant 59$ | $60\leqslant x\leqslant 69$ | $70\leqslant x\leqslant 79$ | $80\leqslant x\leqslant 89$ | $90\leqslant x\leqslant 100$ |
|-----------|-----------------------------|-----------------------------|-----------------------------|-----------------------------|-----------------------------|------------------------------|
| Eighth Grade Students | 0 | 0 | 1 | 11 | 7 | 1 |
| Ninth Grade Students | 1 | 0 | 0 | 7 | 10 | 2 |

(Note: A score of 80 or above indicates excellent physical health, 70-79 indicates good physical health, 60-69 indicates qualified physical health, and below 60 indicates poor physical health.)

$(3)$ Data Analysis:
The mean, median, and mode of the two sets of sample data are shown in the table below. Please complete the table:

|          | Mean | Median | Mode |
|----------|------|--------|------|
| Eighth Grade | 78.3 | 77.5 | ①______ |
| Ninth Grade | 78 | ②______ | 81 |

$(4)$ Conclusion:
① Estimate the number of students in the ninth grade who have excellent physical health to be ______.
② It can be inferred that ______ students in each grade have better physical health. The reason is ______. (Provide at least two different perspectives to explain the reasonableness of the inference.)

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