
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
Given that the probability of each cannon hitting the target is $0.5$, there are $10$ cannons simultaneously firing at a target once each. Let $A$ denote the probability of hitting the target exactly $3$ times; if hitting the target scores $2$ points, and the expected value of the total score of the $10$ cannons is denoted by $B$, calculate the values of $A$ and $B$.

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