
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
(The full score of this question is 14 points)  
Suppose the probabilities of A, B, and C hitting the target in each shot are 0.7, 0.6, and 0.5, respectively.  
Each of the three shoots at the target once, calculate the probability that at least one person hits the target;  
Each of the three shoots at the target once, calculate the probability that exactly two people hit the target;  
If A shoots at the target three times alone, calculate the probability that he hits the target exactly twice.

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