
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 three table tennis associations, A, B, and C, with 27, 9, and 18 athletes, respectively. Six athletes are to be selected for a competition using stratified sampling.

(I) Determine the number of athletes to be selected from each association;

(II) The selected 6 athletes are numbered A$_{1}$, A$_{2}$, A$_{3}$, A$_{4}$, A$_{5}$, A$_{6}$. Two athletes are randomly selected from these 6 for a doubles match.

(i) List all possible outcomes;

(ii) Let $A$ be the event "at least one of the athletes numbered A$_{5}$ and A$_{6}$ is selected". Compute the probability of event $A$.

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