
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
(5 points) If the graph of the function $f(x)$ is continuous on an interval, consider the following statements:  
① If $f(a) \cdot f(b) < 0$, then $f(x)$ has exactly one zero on the interval;  
② If $f(a) \cdot f(b) < 0$, then $f(x)$ has at least one zero on the interval;  
③ If $f(a) \cdot f(b) > 0$, then $f(x)$ has no zeros on the interval;  
④ If $f(a) \cdot f(b) > 0$, then $f(x)$ may have zeros on the interval.  
Among these statements, the correct ones are (Fill in the correct statement numbers).

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