
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 participated in a popular science knowledge competition and needed to answer three questions. The rules of the competition stipulate that each correct answer earns 100 points, while each incorrect answer deducts 100 points. Assuming that the student has a probability of 0.8 of answering each question correctly, and that the correctness of each question is independent of the others.<br/>$(Ⅰ)$ Find the probability distribution and mathematical expectation of the total score $\xi$ of the student answering these three questions;<br/>$(Ⅱ)$ Find the probability that the student's total score is not negative (i.e., $\xi \geqslant 0$).

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