
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]


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Three table tennis associations, A, B, and C, have 27, 9, and 18 athletes, respectively. A stratified sampling method is used to select 6 athletes from these three associations to form a team for a competition.

1. Determine 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. From these 6 athletes, 2 are randomly selected to participate in a doubles match.
   1. List all possible outcomes using the given numbers.
   2. Let event A be "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}
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