
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
Which of the following statements is correct?  
① The graph of a power function must pass through the origin.  
② When $a<0$, the power function $y=x^a$ is a decreasing function.  
③ When $a>1$, the power function $y=x^a$ is an increasing function.  
④ The function $y=x^2$ is both a quadratic function and a power function.

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