
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
Given the following four pairs of events:
1. A person shoots once, "hits the 7th ring" and "hits the 8th ring";
2. Person A and person B each shoot once, "at least one person hits the target" and "A hits the target, but B does not";
3. Drawing 2 balls from a bag containing 2 red balls and 2 black balls, "at least one black ball" and "both are red balls";
4. Drawing 2 balls from a bag containing 2 red balls and 2 black balls, "no black balls" and "exactly one red ball";
Among these, the mutually exclusive events are \_\_\_\_\_\_ . (Fill in the numbers of the propositions you think are correct)

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