
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 shooting competition, participants A and B each fire one bullet in a round. According to past data, the probabilities of A hitting the 8, 9, and 10 rings are 0.6, 0.3, and 0.1, respectively, while the probabilities of B hitting the 8, 9, and 10 rings are 0.4, 0.4, and 0.2, respectively.  
Assume that A and B's shooting are independent of each other.  
(Ⅰ) Calculate the probability that A hits more rings than B in a round;  
(Ⅱ) Calculate the probability that in three independent rounds, A hits more rings than B in at least two rounds.

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