
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 probability distribution of a random variable $\xi$ as shown in the table below, where $x > 0$, $y > 0$, find the mathematical expectation of the random variable $\xi$, $E\xi =$____.

| $x_{i}$ | $1$ | $2$ | $3$ |
|---------|-----|-----|-----|
| $P(\xi =x_{i})$ | $x$ | $y$ | $x$ |

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