
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:
- Proposition ①: The minimum value of $y= \frac{x^2+3}{\sqrt{x^2+2}}$ is $2$;
- Proposition ②: If $a > b$, then $\frac{1}{a} < \frac{1}{b}$ holds if and only if $ab > 0$;
- Proposition ③: If the inequality $x^2+ax-4 < 0$ holds for any $x \in (-1,1)$, then the range of $a$ is $(-3,3)$.

The correct proposition number(s) is/are ______. (Write down all correct proposition numbers)

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