
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
A student conducted a social practice activity during winter vacation to analyze the relationship between the average daytime temperature and the sales volume of a certain drink in a milk tea shop. The student recorded the average daytime temperature $x$ (in Celsius) and the sales volume $y$ (in cups) of this drink in the milk tea shop from January 11 to January 15, and obtained the following data:

1. Based on the given five sets of data, find the linear regression equation of $y$ with respect to $x$, denoted as $\hat{y}=\hat{b}x+\hat{a}$.
2. Using the linear regression equation obtained in question 1, if the weather forecast predicts an average daytime temperature of 7°C on January 16, predict the sales volume of this drink in the milk tea shop.

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

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