
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 and knowledge competition and needs to answer 3 questions. According to the competition rules: answering the 1st, 2nd, and 3rd questions correctly scores 100 points, 100 points, and 200 points, respectively, while incorrect answers score zero points. Assuming the probabilities of this student answering the 1st, 2nd, and 3rd questions correctly are 0.8, 0.7, and 0.6, respectively, and the correctness of each answer is independent of the others.  
(1) Calculate the probability of this student scoring 200 points;  
(2) If scoring at least 300 points is considered passing, calculate the probability of this student passing the competition.

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