
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 shopping mall is holding a prize promotion event, where customers can participate in a lottery after purchasing a certain amount of goods. There are two plans to choose from for the lottery.

Plan 1: Draw 2 balls at random from an opaque box containing 4 red balls and 2 white balls. If the 2 balls drawn are both red, then you win a prize; otherwise, you do not win.

Plan 2: Roll 2 dice. If at least one of the numbers shown is 4, then you win a prize; otherwise, you do not win. (Note: The dice (or balls) are identical in size, shape, and texture.)

(I) Some customers believe that in Plan 1, because the number of red balls is greater than the number of white balls, the probability of winning is greater than $\dfrac{1}{2}$. Do you think this is correct? Please explain your reasoning.

(II) If you were to participate in the lottery, which plan would you choose? Please explain your reasoning.

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