
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 propositions:  
(1) If A is a random event, then $0 \leq P(A) \leq 1$  
(2) If event A is a certain event, then A and B are necessarily complementary events  
(3) If events A and B are mutually exclusive, then A and B are necessarily complementary events  
(4) If events A and B are complementary events, then A and B are necessarily mutually exclusive events  
Among these, the correct proposition numbers are.

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