
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
Definition: For a mapping $f: A \rightarrow B$, if different elements in $A$ have different images, and every element in $B$ has a pre-image, then $f: A \rightarrow B$ is called a one-to-one mapping. If there exists a correspondence $\varphi$ that makes $A$ to $B$ a one-to-one mapping, then $A$ and $B$ are said to have the same cardinality. Consider the following propositions:  
① $A=\{\text{odd numbers}\}$, $B=\{\text{even numbers}\}$, then $A$ and $B$ have the same cardinality;  
② There are two concentric circles, $A$ is the set of all points on the smaller circle, $B$ is the set of all points on the larger circle, then $A$ and $B$ do not have the same cardinality;  
③ If $A$ is a proper subset of $B$, then $A$ and $B$ cannot have the same cardinality;  
④ If $A$ and $B$ have the same cardinality, and $B$ and $C$ have the same cardinality, then $A$ and $C$ have the same cardinality.  
Among these, the true propositions are.

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