
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
A track and field team has three sprinters. According to the statistics from their usual training sessions, the probabilities of sprinters A, B, and C finishing a 100m dash within 13 seconds (considered qualified) are $\frac{2}{5}$, $\frac{3}{4}$, and $\frac{1}{3}$, respectively. If the performance of these three sprinters in a 100m dash is tested once, then:  
① The probability that all three are qualified;  
② The probability that two are qualified;  
③ The probability that at least one is qualified.

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