
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 a certain season, two basketball players, A and B, scored in each game as shown in the table below:

|       | Game 1 | Game 2 | Game 3 | Game 4 | Game 5 | Game 6 | Game 7 |
|-------|--------|--------|--------|--------|--------|--------|--------|
| A     | 26     | 28     | 32     | 22     | 37     | 29     | 36     |
| B     | 26     | 29     | 32     | 28     | 39     | 29     | 27     |

$(1)$ Calculate the average score and variance of player A and player B in these seven games, and determine whose score is more stable.  
$(2)$ Given that the scores of player A and player B in each game are independent of each other, if a score higher than 30 is considered excellent, estimate the probability using frequency to assess the probability that both player A and player B will perform excellently in the eighth game.

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