
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]


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A certain pharmaceutical company has developed a new drug to treat a certain disease, with a cure rate of $p$. The drug is now used to treat $10$ patients, and the number of patients cured is denoted as $X$.  
$(1)$ If $X=8$, two patients are randomly selected from these $10$ people for drug interviews. Find the distribution of the number of patients cured, denoted as $Y$, among the selected patients.  
$(2)$ Given that $p\in \left(0.75,0.85\right)$, let $A=\{k\left|\right.$ probability $P\left(X=k\right)$ is maximum$\}$, and $A$ contains only two elements. Find $E\left(X\right)$.

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