
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
The following are four propositions: 
① The negation of the proposition "Triangles of equal area are congruent";
② The inverse of the proposition "If $xy=1$, then $x$ and $y$ are reciprocals of each other";
③ The contrapositive of the proposition "If $A\cap B=B$, then $A \subseteq B$";
④ The contrapositive of the proposition "If $m>1$, then the equation $x^2-2x+m=0$ has real roots".
Among these, which propositions are true (fill in the number(s) of the correct proposition(s)).

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