
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 takes exams in 3 courses. Suppose the probabilities of the student achieving excellent grades in these three courses are $\frac{4}{5}$, $\frac{3}{5}$, and $\frac{2}{5}$, respectively, and the outcomes of achieving excellent grades in different courses are independent of each other.

(1) Calculate the probability that the student achieves excellent grades in at least one course.

(2) Calculate the probability that the student achieves excellent grades in exactly one course.

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