
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
Since the beginning of the year 2023, "retaliatory tourism" has become a synonym for the strong recovery of the tourism industry. Zhangzhou, with its rich tourism resources, profound cultural heritage, and a wide variety of traditional Minnan snacks, attracts tourists from all over. In order to explore and promote the local culture of Zhangzhou, a school organized a knowledge competition with the theme "I Love Zhangzhou," with 20 students from Class 8-1 and 20 students from Class 8-2 participating. The results are as shown in the table below:

| Score | 70 | 75 | 80 | 85 | 90 | 95 | 100 |
|-------|----|----|----|----|----|----|-----|
| Class 8-1 | 2 | 4 | 3 | 1 | 5 | 3 | 2 |
| Class 8-2 | 0 | 2 | 5 | 8 | 2 | 2 | 1 |

Teacher Wu made the following analysis based on the table above:

|         | Mean | Median | Mode | Variance |
|---------|------|--------|------|----------|
| Class 8-1 | 85 | $a$ | 90 | 90 |
| Class 8-2 | $b$ | 85 | 85 | 40 |

$(1)$ Find the median $a$ of Class 8-1 in the grade statistics table;<br/>$(2)$ Find the mean $b$ of Class 8-2 in the grade statistics table;<br/>$(3)$ Which class sent students with more stable grades? Why?

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