
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
Recently, a chip development team announced that they have independently developed the advanced multidimensional packaging technology $XDFOI$, which can package a $4nm$ mobile $SOC$ chip. This is another major breakthrough in Chinese chip technology, which is of great significance for the development of Chinese chips. It can be said that the breakthrough in domestic $4nm$ advanced packaging technology has stimulated the potential of Chinese chips, proving that as the well-known academician Ni Guangnan said, advanced technology cannot be bought or begged for, and independent research and development is the ultimate way out. The research team is preparing to recruit talents at a famous university in China and has prepared $3$ test questions. To be hired, one needs to answer at least two questions correctly. Two candidates, A and B, have applied for the test. The probability of each of them answering each question correctly is $p\left(0 \lt p \lt 1\right)$, and the events are independent. If candidate A chooses all $3$ questions and candidate B randomly selects $2$ questions to answer, answer the following questions:
$(1)$ Find the probability of A and B being hired respectively;
$(2)$ Let the number of people hired from A and B be $\xi$, determine if there exists a unique value of $p$ denoted as $p_{0}$, such that $E\left(\xi \right)=1.5$? Explain the reason.

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