
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 department store is holding a promotional lottery where customers can participate after purchasing a certain amount of goods. There are two lottery options to choose from:
Option one: Draw two balls at random from an opaque box containing four red balls and two white balls. Win if the two balls drawn are both red, otherwise, it is not a win.
Option two: Roll two dice. Win if at least one of the dice shows a four, otherwise, it is not a win. (Note: The dice (or balls) are identical in size, shape, and texture.)
(Ⅰ) Some customers believe that in option one, the probability of winning is greater than $\frac{1}{2}$ since the number of red balls in the box is more than the number of white balls. Do you think this is correct? Please explain your reasoning;
(Ⅱ) If you were to participate in the lottery, which option would you choose? Please explain your reasoning.

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