
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
In a cabinet, there are 3 pairs of different shoes. If 2 shoes are randomly taken out, let event A denote "the taken out shoes do not form a pair"; event B denote "both taken out shoes are for the same foot"; event C denote "one shoe is for the left foot and the other is for the right foot, but they do not form a pair".

(Ⅰ) Please list all the basic events;  
(Ⅱ) Calculate the probabilities of events A, B, and C respectively.

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