
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 corresponding data between the expenditure $x$ (in units of 10,000 yuan) on a certain product's live platform and the sales amount $y$ (in units of 10,000 yuan) of agricultural products as shown in the table below:

| $x$ | $2$ | $3$ | $4$ | $6$ | $7$ | $8$ |
|-----|-----|-----|-----|-----|-----|-----|
| $y$ | $7.5$ | $11.5$ | $m$ | $31.5$ | $36.5$ | $43.5$ |

It is known that the linear regression equation obtained from the table is $\hat{y}=6x+\hat{a}$. Due to an operator error, one data point is missing. However, it is known that $({\overline{x},\overline{y}})$ lies on the graph of the function $y=x^{2}$. Based on this estimation, the value of $m$ is ________; when an investment of $12$ thousand yuan is made, the sales amount is approximately ________ thousand yuan.

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