
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 the distribution table of the random variable $\xi$ as shown in the table below, when $\frac{1}{x}+\frac{4}{y}$ reaches its minimum value, $x=\_\_\_\_\_\_$, $E\left(\xi \right)=\_\_\_\_\_\_$.

| $\xi$ | 1   | 2   | 3   |
|-------|-----|-----|-----|
| $P$   | $x$ | $\frac{1}{2}$ | $y$ |

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