
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
The corresponding data between the price $x$ (unit: ten thousand dollars per ton) of a certain product and the demand $y$ (unit: tons) are shown in the table below:

| $x$ | $12$ | $11$ | $10$ | $9$ | $8$ |
|-----|------|------|------|-----|-----|
| $y$ | $5$  | $6$  | $8$  | $10$| $11$|

(1) Given that a linear regression model can be used to fit the relationship between $y$ and $x$, find the linear regression equation of $y$ with respect to $x$.

(2) Predict whether the demand will exceed $15$ tons when the price of the product is set at $6$ ten thousand dollars, and explain the reason.

Reference formula: $\hat{a}=\overline{y}-\hat{b}\overline{x}$, $\hat{b}=\frac{\sum_{i=1}^{n}{({x}_{i}-\overline{x})}({y}_{i}-\overline{y})}{\sum_{i=1}^{n}{{({x}_{i}-\overline{x})}^{2}}}$.

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