
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 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 lie in the fourth quadrant; ③ When n=0, the graph of the function $y=x^n$ is a straight line; ④ The power function $y=x^n$, when $n>0$, is an increasing function; ⑤ The power function $y=x^n$, when $n<0$, decreases in the first quadrant as the value of x increases. The correct propositions are: (Fill in the sequence numbers of the propositions you think are correct).

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