
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
Three products are selected from a batch of products. Let $A=$ {all three products are not defective}, $B=$ {all three products are defective}, and $C=$ {not all three products are defective}. The correct sequence number(s) of the following conclusions is/are _______.
(1) $A$ and $B$ are mutually exclusive;
(2) $B$ and $C$ are mutually exclusive;
(3) $A$ and $C$ are mutually exclusive;
(4) $A$ and $B$ are contradictory;
(5) $B$ and $C$ are contradictory.

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