
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 class teacher conducted a survey on the learning enthusiasm and attitude towards class work of 50 students. The statistical data is shown in the table below:
\[
\begin{array}{|l|c|c|c|}
\hline
 & Actively Participate in Class Work & Not Actively Participate in Class Work & Total \\
\hline
High Learning Enthusiasm & 17 & 8 & 25 \\
\hline
Moderate Learning Enthusiasm & 5 & 20 & 25 \\
\hline
Total & 22 & 28 & 50 \\
\hline
\end{array}
\]

(1) If a student is randomly selected from the class, what is the probability of selecting a student who actively participates in class work? What is the probability of selecting a student who does not actively participate in class work and has moderate learning enthusiasm?

(2) Using the method of independence test analysis, determine if there is a relationship between students' learning enthusiasm and their attitude towards class work, and explain the reasoning. The reference table is provided below:
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline
P\left(k^{2} \geqslant k_{0}\right) & 0.50 & 0.40 & 0.25 & 0.15 & 0.10 & 0.05 & 0.010 & 0.005 & 0.001 \\
\hline
k_{0} & 0.455 & 0.708 & 1.323 & 2.072 & 2.706 & 3.841 & 6.635 & 7.879 & 10.8 \\
\hline
\end{array}
\]

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