
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
Place three balls, numbered 1, 2, and 3, into three boxes labeled A, B, and C, with each box receiving one ball. It is known that the probabilities of ball 1 being placed in box A, ball 2 in box B, and ball 3 in box C are $\frac{3}{5}$, $\frac{1}{2}$, and $p$, respectively. Let the event of ball 1 being placed in box A be event A, ball 2 in box B be event B, and ball 3 in box C be event C. Events A, B, and C are independent.  
(Ⅰ) If $p= \frac{1}{2}$, calculate the probability that at least two of the events A, B, and C occur;  
(Ⅱ) If the probability of exactly two out of the events A, B, and C occurring is not less than $\frac{2}{5}$, find the range of values for $p$.

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