
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
There are 10 balls of the same size in a box, including 2 red balls, 4 black balls, and 4 white balls. The rule is: if you draw 3 balls at a time and they are all the same color, you win a reward of 10 yuan; otherwise, you are fined 2 yuan.  
(I) If a person draws once, find the probability that they will win a reward;  
(II) If 10 people participate in the ball drawing game, each person draws once and then returns the ball, let the random variable $\xi$ be the number of people who win a reward,  
(i) find $P(\xi > 1)$, (ii) find the expected amount of money won by these 10 people. (Give the result as a fraction, reference data: $(\frac{14}{15})^{10} \approx \frac{1}{2}$)

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