
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 propositions:  
(1) Complementary events must be mutually exclusive events.  
(2) If $A$ and $B$ are two events, then $P(A \cup B) = P(A) + P(B)$.  
(3) If events $A$, $B$, and $C$ are pairwise mutually exclusive, then $P(A) + P(B) + P(C) = 1$.  
(4) If events $A$ and $B$ satisfy $P(A) + P(B) = 1$, then $A$ and $B$ are complementary events. Determine the number of incorrect propositions.

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