
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
During the global financial crisis, which also affected the Chinese stock market, four individuals, A, B, C, and D, plan to take advantage of the current market downturn to "buy the dip". They agree to each randomly purchase one out of the six designated stocks (assuming that each stock is in the same condition when purchased).

(1) Calculate the probability that all four individuals happen to buy the same stock;

(2) Calculate the probability that at most two of the four individuals buy the same stock.

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