
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 table below shows the Gross Domestic Product (GDP) of China from 2012 to 2018 in trillion US dollars:

| Year | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |
|------|------|------|------|------|------|------|------|
| Year Code $x$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| GDP $y$ (trillion US dollars) | 8.5 | 9.6 | 10.4 | 11 | 11.1 | 12.1 | 13.6 |

$(1)$ From the data in the table, it is known that there is a strong linear correlation between $x$ and $y$. Find the linear regression equation with $x$ as the explanatory variable and $y$ as the predicted variable.  
$(2)$ Given that the GDP of the United States in 2018 was approximately 20.5 trillion US dollars, using the conclusion from part (1), determine in which year China could surpass the GDP of the United States in 2018.  
Reference data: $\sum_{i=1}^7{y_i}=76.3$, $\sum_{i=1}^7{y_i}{x_i}=326.2$  
Reference formulas: The least squares estimates for the slope and intercept in the regression equation $\hat{y}=\hat{b}x+\hat{a}$ are:  
$\hat{b}=\frac{\sum_{i=1}^n{(y_i-\overline{y})(x_i-\overline{x})}}{\sum_{i=1}^n{(x_i-\overline{x})^2}}=\frac{\sum_{i=1}^n{y_ix_i-n\overline{y}\overline{x}}}{\sum_{i=1}^n{x_i^2-n\overline{x}^2}}$  
$\hat{a}=\overline{y}-\hat{b}\overline{x}$.

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