
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
Select $10$ students from Grade 7 Class 1 and Class 2 respectively for a shooting competition. According to the rules, each person shoots $10$ balls. The number of goals scored by the players from the two classes is shown in the table below. Answer the questions based on the data in the table.

| Goals Scored | Number of Students | Class |
|--------------|--------------------|-------|
| 10           | 1                  | Class 1 |
| 9            | 1                  | Class 1 |
| 8            | 1                  | Class 1 |
| 7            | 4                  | Class 1 |
| 6            | 0                  | Class 1 |
| 5            | 3                  | Class 1 |
| 10           | 0                  | Class 2 |
| 9            | 1                  | Class 2 |
| 8            | 2                  | Class 2 |
| 7            | 5                  | Class 2 |
| 6            | 0                  | Class 2 |
| 5            | 2                  | Class 2 |

$(1)$ Calculate the mean, mode, and median of the number of goals scored by the players in Class 1 and Class 2 respectively.  
$(2)$ If one class has to be selected as the representative of the grade for the school's team shooting competition, which class would you choose?  
$(3)$ If aiming to be in the top three in terms of individual goals scored in the school, which class should be chosen?

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