
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 $x$ and $y$ are two variables with linear correlation, and their values are as shown in the table below:

| $x$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|-----|-----|-----|-----|-----|-----|
| $y$ | $4$ | $m$ | $9$ | $n$ | $11$ |

If the regression line is $\hat{y}=\hat{b}x+\hat{a}$ passing through the point $(3,7)$, then the conditions satisfied by $m$ and $n$ are ____.

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