
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]


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Among the following propositions:  
① The graph of a power function passes through the points (1,1) and (0,0);  
② The graph of a power function cannot be in the fourth quadrant;  
③ When $n=0$, the graph of the function $y=x^n$ is a straight line;  
④ For the power function $y=x^n$, when $n>0$ it is an increasing function;  
⑤ For the power function $y=x^n$, when $n<0$, the value of the function decreases as the value of $x$ increases in the first quadrant.  
The correct proposition numbers are: \_\_\_\_\_\_\_\_ (Fill in the numbers of the propositions you think are correct)

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