
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
In a major international sports event, an athlete signed up to participate in 5 competitions. Given that the athlete's probability of breaking the world record in each of these 5 competitions is 0.8, calculate:

(1) The probability that the athlete breaks at least 3 world records;
(2) The mathematical expectation $E\xi$ (i.e., the mean) of the number of world records $\xi$ broken by the athlete.

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