
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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In the table tennis associations A, B, and C, the number of athletes is 27, 9, and 18, respectively. We use stratified sampling to select 6 athletes from these associations to form a team for a competition.  
(1) Determine the number of athletes to be selected from each association.  
(2) Upon selecting 6 athletes, they are labeled as $A_1$, $A_2$, $A_3$, $A_4$, $A_5$, $A_6$. Randomly choose 2 athletes from these 6 to participate in a doubles match.  
(i) List all the possible outcomes using the given labels.  
(ii) Let event A be the event that "at least one of the athletes with labels $A_5$ and $A_6$ is chosen." Calculate the probability of event A occurring.

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