
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
Determine which of the following statements are true:
1. $y=1$ is a power function;
2. An odd function $y=f(x)$ defined on $\mathbb{R}$ satisfies $f(0)=0$;
3. The function $f(x)=\lg(x+ \sqrt{x^2+1})$ is an odd function;
4. For $a<0$, $(a^2)^{\frac{3}{2}}=a^3$;
5. The function $y=1$ has two zeros;
List all the correct statement numbers.

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