
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
Given the following propositions:
(1) The graph of the power function passes through the points (1, 1) and (0, 0);
(2) The graph of the power function can never be a straight line;
(3) When n=0, the graph of the function y=x^n is a straight line;
(4) The power function y=x^n is increasing when n>0;
(5) The power function y=x^n is decreasing in the first quadrant when n<0 as the value of x increases. The correct proposition numbers are ___.

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