
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 statements, the number of correct ones is $\boxed{0}$  
① If $f'(x)=0$, then $x$ is an extremum point of $f(x)$.  
② On the closed interval $[a, b]$, the largest among the local maxima is the maximum value.  
③ If the local maximum of $f(x)$ is $f(x_1)$, and the local minimum of $f(x)$ is $f(x_2)$, then $f(x_1) > f(x_2)$.  
④ Some functions may have two minimum values.  
⑤ If $x$ is an extremum point of $f(x)$, then $f'(x)$ exists and $f'(x)=0$.

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