
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
To enrich students' extracurricular activities, the school holds basketball, soccer, and badminton competitions. After the preliminary and semifinal rounds, classes A and B have entered the finals. In the finals, the winning team of each event earns 8 points, while the losing team earns 0 points, with no draws. The class with the highest total score after the three events wins the championship. It is known that the probabilities of class A winning in basketball, soccer, and badminton are 0.4, 0.8, and 0.6, respectively, and the results of each event are independent. Find:  
(1) The probability of class A winning the championship.  
(2) Let X represent the total score of class B. Find the distribution table and expectation of X.

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