
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
Online shopping, as a new way of consumption, is widely recognized by consumers for its advantages such as speed, a wide variety of products, and high cost performance. A certain online shopping company has compiled data on the number of people who have shopped on their website in the past five years. The relevant data is as follows (where "$x=1$" represents the year $2015$, "$x=2$" represents the year $2016$, and $x$ is an integer, and so on; $y$ represents the number of people): 

| $x$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|-----|-----|-----|-----|-----|-----|
| $y$ (in ten thousand) | $20$ | $50$ | $100$ | $150$ | $180$ |

According to the data in the table, we can calculate $\hat{b}=\frac{1920-5\times3\times100}{55-5\times9}=42$. If it is predicted that the number of online shoppers in this company will exceed $300$ thousand, then the minimum value of $x$ is ______.

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