
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
Jia, Yi, and Bing are three individuals planning to enter the stock market during its current downturn. If each person randomly buys one out of the ten designated stocks (assuming each stock has completely identical fundamental conditions when purchasing), calculate:
(1) The probability that Jia, Yi, and Bing each buy exactly the same stock.
(2) The probability that at least two out of Jia, Yi, and Bing buy the same stock.

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