
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 company has 100,000 yuan for investment. If the company invests in Project A, market analysis indicates that after one year, the possible outcomes are a 10% profit, a 10% loss, or no change, with probabilities of $\frac{1}{2}$, $\frac{1}{4}$, and $\frac{1}{4}$, respectively. If the company invests in Project B, after one year, the possible outcomes are a 20% profit or a 20% loss, with probabilities $\alpha$ and $\beta$ (where $\alpha + \beta = 1$).

(1) If 100,000 yuan is invested in Project A, let $\xi$ represent the investment return (return = recovered funds - invested funds). Find the probability distribution of $\xi$ and $E\xi$.
(2) If the average return from investing 100,000 yuan in Project B is not lower than the average return from investing in Project A, determine the range of values for $\alpha$.

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