
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]


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Assume that for a certain device, the relationship between its service life $x$ (in years) and the maintenance cost $y$ (in ten thousand yuan) is given by the following statistical data $(x_i, y_i)$ ($i=1,2,3,4,5$). It is known that $y$ is linearly related to $x$, and the average values of the five sets of data are $\bar{x}=4$ and $\bar{y}=5.4$. If the linear regression equation $\hat{y} = bx + a$ is used to estimate, and the maintenance cost for using the device for 8 years is 1.1 ten thousand yuan more than for using it for 7 years,  
(1) Find the equation of the regression line; (2) Estimate the maintenance cost when the service life is 10 years.

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