
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
Two players, A and B, are playing table tennis. The rules are as follows: winning a game earns 3 points, drawing earns 1 point, and losing earns 0 points. It is known that A and B have played three games in total.  
$(1)$ Represent the scores of A and B when A wins all three games as $(9,0)$. Write down all possible score combinations for A and B, and calculate the probability that the sum of their scores is 9 points.  
$(2)$ If A and B play a best-of-three match, with A winning a game with a probability of 0.6 and B winning with a probability of 0.4. Using a computer simulation experiment: generate random numbers between 1 and 5, where 1, 2, or 3 represent A winning a game, and 4 or 5 represent B winning a game. Since three games are played, each set of three random numbers represents one match. Twenty sets of random numbers have been generated:  
$123 344 423 114 423 453 354 332 125 342$  
$534 443 541 512 152 432 334 151 314 525$  
① Estimate the approximate probability of A winning using the above random numbers.  
② Calculate the probability of A winning.

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