
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
Define the characteristic function of a subset $A$ of the universal set $U$ as $$f_{A}(x)= \begin{cases} 1, & x\in A \\ 0, & x\in C_{U}A\end{cases}$$, where $C_{U}A$ denotes the complement of $A$ in the universal set $U$. For the sets $A, B \subseteq U$, the correct statements among the following are \_\_\_\_\_\_ .  
(1) $A \subseteq B \Rightarrow f_{A}(x) \leq f_{B}(x)$  
(2) $f_{C_{U}A}(x) = 1 - f_{A}(x)$  
(3) $f_{A \cap B}(x) = f_{A}(x) \cdot f_{B}(x)$  
(4) $f_{A \cup B}(x) = f_{A}(x) + f_{B}(x)$

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