
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 school organized a math competition with $4$ mandatory questions. Each correct answer earns $4$ points, and each wrong answer deducts $2$ points. Student A participated in this activity, assuming that the probability of A answering each question correctly is $\frac{3}{4}$, and the correctness of each question does not affect the others. Let $Y$ be the number of questions A answered correctly, and let $X$ be the total score of A after completing the $4$ questions.
$(Ⅰ)$ Establish the functional relationship between $X$ and $Y$, and find $P\left(X \lt 0\right)$;
$(Ⅱ)$ Find the distribution table of $X$ and $E\left(X\right)$.

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