
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
Which of the following propositions are correct?

① The locus of points whose distances to two fixed points F<sub>1</sub> and F<sub>2</sub> sum to a constant length is an ellipse.
② The contrapositive of the statement "If ab=0, then a=0 or b=0" is "If a≠0 and b≠0, then ab≠0".
③ If f′(x)=0, then f(x) is an extreme value of f(x).
④ The curve y=2x<sup>3</sup> - 3x<sup>2</sup> has exactly two extreme values.

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