
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 $f(x)=\sin \left(2x- \frac{\pi}{3}\right)$ is an odd function;

2. The function $f(x)=\cos \left(2x- \frac{\pi}{3}\right)$ has an axis of symmetry with the equation $x= \frac{\pi}{3}$;

3. For the function $f(x)= \sqrt{2}\sin \left(2x+ \frac{\pi}{4}\right)$, where $x\in\left[0, \frac{\pi}{2}\right]$, the range of $f(x)$ is $\left[0, \sqrt{2}\right]$;

4. The function $f(x)= \frac{\cos x+3}{\cos x}$, where $x\in\left(- \frac{\pi}{2}, \frac{\pi}{2}\right)$, has a minimum value but no maximum value.

The correct statement(s) is/are __________.

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