
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 the following four propositions, the correct proposition numbers are __________  
① The graph of the function $y=\tan x$ is symmetric about the point $\left(\frac{k\pi}{2}, 0\right)$, where $k\in \mathbb{Z}$.  
② The function $y=\sin |x|$ has the smallest positive period of $\pi$.  
③ If $\theta$ is an angle in the second quadrant, then $\tan \frac{\theta}{2} > \cos \frac{\theta}{2}$ and $\sin \frac{\theta}{2} > \cos \frac{\theta}{2}$.  
④ The minimum value of $y=\cos^2x+\sin x$ is $-1$.

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