
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
Among the following propositions,
① Power functions are increasing functions in the first quadrant;
② The graph of a power function passes through the points (0, 0) and (1, 1);
③ If the power function $y=x^a$ is an odd function, then $y=x^a$ is an increasing function on its domain;
④ The graph of a power function cannot appear in the fourth quadrant.
The correct proposition number is.

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