
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 that the function $f(x)$ is defined on the set of real numbers $\mathbb{R}$, consider the following statements:  
① If there exists a constant $x$ such that $f′(x)=0$, then the function $f(x)$ must have an extremum at $x$;  
② If the function $f(x)$ has an extremum at $x$, then the function $f(x)$ must be differentiable at $x$;  
③ If the function $f(x)$ is differentiable everywhere on $\mathbb{R}$, then if it has a local minimum, it is the global minimum on $\mathbb{R}$;  
④ If for any $x \neq x_0$, $f(x) > f(x_0)$, then $f(x_0)$ is the global minimum of the function $f(x)$;  
⑤ If for any $x < x_0$, $f′(x) > 0$, and for any $x > x_0$, $f′(x) < 0$, then $f(x_0)$ is a global maximum of the function $f(x)$;  
Among these statements, the correct ones are     .

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