
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:
① The function $f(x)=\sin(2x- \frac{\pi}{3})$ is an odd function;
② The function $f(x)=\cos(2x- \frac{\pi}{3})$ has an axis of symmetry with the equation $x=- \frac{\pi}{3}$;
③ For the function $f(x)= \sqrt{2}\sin(2x+ \frac{\pi}{4})$, where $x\in[0, \frac{\pi}{2}]$, the range of $f(x)$ is $[0, \sqrt{2}]$;
④ The function $f(x)= \frac{\cos x+3}{\cos x}$, where $x\in(- \frac{\pi}{2}, \frac{\pi}{2})$, has a minimum value but no maximum value.
The correct statement numbers are __________.

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