
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
In order to develop students' core literacy and cultivate their comprehensive abilities, a certain middle school utilizes "Sunshine Big Recess" to organize students to actively participate in a variety of extracurricular activities. The school has established a dance team, a soccer team, a basketball team, a shuttlecock team, a shooting team, etc. In a training session of the shooting team, two members, A and B, each fired 10 bullets, and the results were recorded as follows:

| Shooting Order | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|----------------|---|---|---|---|---|---|---|---|---|----|
| A's Score      | 8 | 9 | 7 | 9 | 8 | 6 | 7 | a | 10| 8  |
| B's Score      | 6 | 7 | 9 | 7 | 9 | 10| 8 | 7 | 7 | 10 |

$(1)$ Given that the average score of A and B is $8$, find the value of $a$;  
$(2)$ Find the median of A's scores and the mode of B's scores;  
$(3)$ If the variance of A's scores is $1.2$, find the variance of B's scores and determine who has more stable scores, A or B?

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