
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
There are six propositions below:  
① The smallest positive period of the function $y=\sin^4x-\cos^4x$ is $\pi$;  
② The set of angles whose terminal sides are on the y-axis is $\{\alpha|\alpha= \frac{k\pi}{2}, k\in\mathbb{Z}\}$;  
③ In the same coordinate system, the graph of the function $y=\sin x$ and the graph of the function $y=x$ have three common points;  
④ The function $y=\tan x$ is monotonically increasing in its domain;  
⑤ The function $y=\sin(x- \frac{\pi}{2})$ is an even function;  
⑥ If $\vec{a}\cdot\vec{b}=0$, then $\vec{a}=\vec{0}$ or $\vec{b}=\vec{0}$;  
Among these, the numbers of the true propositions are _______ (write down the numbers of all true propositions).

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