
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 certain precision instrument manufacturer plans to assess the skills of the workers in the factory as follows: each worker produces $10$ consecutive products, and if after inspection there are no fewer than $9$ qualified products, the worker's skill assessment is rated as qualified, and the assessment ends; otherwise, the unqualified products are returned to the worker for debugging. After re-inspection, if all products are qualified, the worker's skill assessment is rated as qualified, and the assessment ends. Otherwise, the worker's skill assessment is rated as unqualified, and training is required. Worker A's probability of producing or debugging each product as qualified is $p\left(0 \lt p \lt 1\right)$, and the production or debugging of each product does not affect each other.<br/>$(1)$ Find the probability that Worker A ends the assessment by producing only $10$ products;<br/>$(2)$ If $X$ represents the total number of products produced and debugged by Worker A, find the expected value $E\left(X\right)$ of the random variable $X$.

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