
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
Among the following pairs of events:  
(1) Athlete A shoots once, "hits 9 rings" and "hits 8 rings",  
(2) Athletes A and B each shoot once, "A hits 10 rings" and "B hits 9 rings",  
(3) Athletes A and B each shoot once, "both A and B hit the target" and "neither A nor B hits the target",  
(4) Athletes A and B each shoot once, "at least one person hits the target" and "A hits the target but B does not hit the target",  
the mutually exclusive events are     and the independent events are     .

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