
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 and B take part in a certain selection test. Among the pool of 10 questions, A has a probability of $\frac{3}{5}$ to answer each question correctly, while B can answer 5 out of the 10 correctly. Each exam randomly selects 3 questions from the pool of 10. For each correct answer, the candidate scores 10 points, and for each incorrect answer (including unanswered), the candidate loses 5 points. A minimum of 15 points is required for selection.  
(1) Find the expected score for A.  
(2) Find the probability that both A and B are selected at the same time.

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