
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 study on the relationship between the temperature difference between day and night in spring and the germination of soybean seeds in a biology research project. He randomly selected 5 days in April for the study and recorded the temperature difference between day and night as well as the number of seeds germinated per 100 seeds soaked each day. The data obtained is as follows:

| Date         | April 1st | April 7th | April 15th | April 21st | April 30th |
|--------------|-----------|-----------|------------|------------|------------|
| Temperature $x/^\circ C$ | 10        | 11        | 13         | 12         | 9          |
| Number of germinated seeds $y/$ seeds | 23        | 25        | 30         | 26         | 16         |

$(1)$ From these 5 days, select any 2 days and find the probability that the number of germinated seeds on those 2 days is not greater than 26.

$(2)$ Based on the data from these 5 days, determine the linear regression equation of $y$ with respect to $x$. The formula for the least squares estimate of the slope of the regression line is given by $b=\frac{{\sum_{i=1}^n({{x_i}-\overline{x}})({{y_i}-\overline{y}})}}{{\sum_{i=1}^n{{({{x_i}-\overline{x}})}^2}}}=\frac{{\sum_{i=1}^n{x_i}{y_i}-n\overline{x}•\overline{y}}}{{\sum_{i=1}^nx_i^2-n{{\overline{x}}^2}}}$.

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