
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
Given the following propositions:  
① If $k>0$, then the equation $x^2+2x-k=0$ has real roots;  
② The negation of "If $a>b$, then $a+c>b+c$";  
③ The inverse of "The diagonals of a rectangle are equal";  
④ The negation of "If $xy=0$, then at least one of $x$ or $y$ is $0$";  
⑤ "If $x\neq2$ or $y\neq3$, then $x+y\neq5$".  
Among these, the numbers of the true propositions are.

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