
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
Consider the following propositions:
- Proposition ①: "If $xy=1$, then $x$ and $y$ are reciprocals of each other" and its converse;
- Proposition ②: "Triangles with equal areas are congruent" and its negation;
- Proposition ③: "If $m \leqslant 1$, then $x^2-2x+m=0$ has real solutions" and its contrapositive;
- Proposition ④: "If $A \cap B = B$, then $A \subseteq B$" and its contrapositive. Among these, the true propositions are __________ (Fill in the serial number).

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