
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 a set of data showing the advertising investment $x$ (in $10,000 yuan) and profit $y$ (in 10,000 yuan) of a certain company's products as shown in the table below:

| $x$ | $2$ | $3$ | $4$ | $5$ | $6$ |
|-----|-----|-----|-----|-----|-----|
| $y$ | $15$ | $21$ | $39$ | $50$ | $75$ |

There is a strong linear relationship between profit $y$ and advertising investment $x$. The linear regression equation is $\hat{y}=14.9x+\hat{a}$. Determine the estimated profit when the advertising investment is $9$ thousand yuan.

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