
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 four propositions:
① The contrapositive of the statement "If $xy=0$, then $x=0$ and $y=0$";
② The negation of the statement "A square is a rhombus";
③ The inverse of the statement "If $ac^2 > bc^2$, then $a>b$";
④ If "For $m>1$, the solution set of the inequality $x^2-2x+m>0$ is $\mathbb{R}$",
identify the false propositions.

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