
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 five propositions, the serial numbers of all true propositions are __________.  
① The function $y=\sin x$ is increasing in the first quadrant.  
② The function $y=\cos\left(x+ \frac{\pi}{2}\right)$ is an odd function.  
③ The graph of the function $y=\tan x$ has its center of symmetry at $(k\pi, 0)$, where $k\in \mathbb{Z}$.  
④ The function $y=\sin |x|$ is a periodic function.  
⑤ The domain of the function $y= \sqrt{\cos(\cos x)}$ is $\mathbb{R}$.

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