
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
Player A and player B have free throw success rates of $\frac{1}{2}$ and $\frac{2}{5}$, respectively.  
(1) If player A and player B each take one free throw, find the probability of exactly one successful shot;  
(2) If player A and player B each take two free throws, find the probability of at least one successful shot in these four attempts.

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