
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 stem-and-leaf plot below records the number of trees planted by four students in groups A and B, respectively. There is one unclear data in group B, represented by X in the plot.

Group A　　　　Group B  
(1) **(For liberal arts)** Calculate the average and variance of the number of trees planted by students in group A;  
**(For science)** If X = 8, calculate the average and variance of the number of trees planted by students in group B;  
(2) If X = 9, randomly select one student from each of the two groups, calculate the probability that the total number of trees planted by these two students is 19.  
(Note: The variance $s^2 = \left[(x_1 - \bar{x})^2 + (x_2 - \bar{x})^2 + \ldots + (x_n - \bar{x})^2\right]$, where $\bar{x}$ is the average of $x_1, x_2, \ldots, x_n$)

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