
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
If $U$ is the universal set, the number of true statements among the following three statements is:

(1) If $A \cap B = \varnothing$, then $(C_U A) \cup (C_U B) = U$  
(2) If $A \cup B = U$, then $(C_U A) \cap (C_U B) = \varnothing$  
(3) If $A \cup B = \varnothing$, then $A = B = \varnothing$

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