
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 that the function $y$ has corresponding values with the independent variable $x$ as shown in the table below:

| $x$ | $\ldots $ | $-5$ | $-2$ | $2$ | $5$ | $\ldots $ |
|-----|-----------|------|------|----|-----|-----------|
| $y$ | $\ldots $ | $-2$ | $m$  | $5$ | $n$ | $\ldots $ |

The following statements are given:
1. If $y$ is an inverse proportion function of $x$, then $2m+5n=0$;
2. If $y$ is a linear function of $x$, then $n-m=7$;
3. If $y$ is a quadratic function of $x$ and the graph opens downwards, then $m \gt n$.

Which of the statements are correct? (Fill in the correct numbers)

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