
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 $f_A(x) = \begin{cases} 1, & x \in A \\ 0, & x \in \complement_U A \end{cases}$, where $\complement_U A$ denotes the complement of set $A$ in the universal set $U$. Given $A \subseteq U$, $B \subseteq U$, consider the following statements:  
① If $A \subseteq B$, then for any $x \in U$, $f_A(x) \leq f_B(x)$;  
② For any $x \in U$, $f_{\complement_U A}(x) = 1 - f_A(x)$;  
③ For any $x \in U$, $f_{A \cap B}(x) = f_A(x) \cdot f_B(x)$;  
④ For any $x \in U$, $f_{A \cup B}(x) = f_A(x) + f_B(x)$.  
Among these statements, the correct ones are \_\_\_\_\_\_. (Write down the numbers of all correct statements)

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