
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 shoots at target A twice, and B shoots at the target once. The probability of A hitting the target with each shot is 0.8, and a hit scores 5 points; the probability of B hitting the target is 0.5, and a hit scores 10 points.
(1) Calculate the probability that A and B together hit the target exactly once;
(2) Let X be the sum of scores obtained by A and B. Find the probability distribution and the expected value of X.

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