
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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A certain shopping mall's sales volume (unit: ten thousand pieces) for five consecutive years is as shown in the table below:

| $x$(year) | 1 | 2 | 3 | 4 | 5 |
|-----------|---|---|---|---|---|
| $y$(sales volume) | 5 | 5 | 6 | 7 | 7 |

$(1)$ Find the linear regression equation $\hat{y}=\hat{b}x+\hat{a}$ for the sales volume $y$ and the corresponding year $x$;  
$(2)$ If two sets of data are randomly selected from the five sets, find the probability that the two selected sets are exactly the data from two consecutive years.  
Note: In the linear regression equation $y=bx+a$, $\hat{b}=\frac{\sum_{i=1}^{n}{{x}_{i}{y}_{i}-n\overline{x}\overline{y}}}{\sum_{i=1}^{n}{{x}_{i}^{2}-n\overline{{x}}^{2}}}$, $\hat{a}=\overline{y}-\hat{b}\overline{x}$. Where $\overline{x}$ and $\overline{y}$ are sample averages, and the linear regression equation can also be written as $\hat{y}=\hat{b}x+\hat{a}$.

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