
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 that the distribution table of the number of rings $\xi$ obtained by a shooter is as follows:

| $\xi$ | $7$ | $8$ | $9$ | $10$ |
|-------|-----|-----|-----|------|
| $P$   | $x$ | $0.1$ | $0.3$ | $y$ |

Calculate the value of $y$, given that the mathematical expectation of $\xi$ is $E(\xi)=8.9$.

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