
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
There are 27, 9, and 18 athletes in three table tennis associations A, B, and C respectively. Now, 6 athletes are selected from these three associations using stratified sampling to form a team for a competition.

(1) Calculate the number of athletes to be selected from each of the three associations.

(2) The selected 6 athletes are numbered A1, A2, A3, A4, A5, and A6. Now, 2 athletes are randomly selected from these 6 to participate in a doubles match.

① List all possible outcomes.

② Let A be the event "At least one of the athletes numbered A5 and A6 is selected". Calculate the probability of event A.

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