
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 5 propositions below:
$(1)$ The minimum positive period of the function $y=\sin ^{4}x-\cos ^{4}x$ is $\pi$;
$(2)$ The set of angles whose terminal side lies 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 a monotonically increasing function on its domain;
$(5)$ The function $y=\sin (x- \frac {\pi}{2})$ is an even function;
The correct proposition numbers are $\_\_\_\_\_\_$.

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