
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 $y=f(x)$ is an odd function defined on $\mathbb{R}$, and $y=f\left(x+ \frac{\pi}{2}\right)$ is an even function, there are several descriptions about the function $y=f(x)$:  
① $y=f(x)$ is a periodic function;  
② $x=\pi$ is a symmetry axis of it;  
③ $(-\pi, 0)$ is a symmetry center of its graph;  
④ $x= \frac{\pi}{2}$ is a symmetry axis of it.  
Among these descriptions, the correct ones are \_\_\_\_\_\_.

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