
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 box, there are 6 ballpoint pens: 3 are black, 2 are blue, and 1 is red. Three pens are randomly selected from the box.  
(1) How many basic events are there in this experiment? If the 3 black ballpoint pens are labeled as A, B, C, the 2 blue ballpoint pens as d, e, and the 1 red ballpoint pen as x, and a basic event is denoted as {a, b, c}, list all the basic events of this experiment;  
(2) What is the probability of selecting exactly one black pen?  
(3) What is the probability of selecting at least one blue pen?

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