
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
Athletes A and B each attempt to high jump a height of 2 meters, with the probabilities of success for each attempt being 0.7 and 0.6, respectively. Assume that the outcomes of their attempts are independent of each other. Calculate:  
(I) The probability that athlete A succeeds on the third attempt for the first time;  
(II) The probability that at least one of the two athletes succeeds in their first attempt;  
(III) The probability that, after two attempts each, athlete A has exactly one more successful attempt than athlete B.

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