
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
Among the following propositions, the true ones are (select all the serial numbers of true propositions):
① The negation of "In the same triangle, the larger side faces the larger angle"
② The converse of "If $m<2$, then $x^2-2x+m=0$ has real roots"
③ The contrapositive of "If $A \cap B = B$, then $A \cup B = A$"
④ "$(x+3)^2+(y-4)^2=0$" is a necessary condition for "$(x+3)(x-4)=0$" to hold.

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