
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 participates in a science popularization knowledge contest, which involves answering three questions. The competition rules are as follows: for each correct answer, the student earns 30 points; for each incorrect or unanswered question, the student loses 30 points. Assuming the probability of answering each question correctly is 0.8, and the correctness of answers to different questions is independent,  
(1) Determine the probability distribution of the student's total score X for these three questions;  
(2) If a total score of at least 30 points qualifies the student to advance to the next round, find the probability that the student advances.

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