
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 game has the following rule: in level \( n \), you roll a die \( n \) times. If the sum of the points from these \( n \) rolls is greater than \( 2^n \), you win that level.

(I) What is the maximum number of levels a participant can win in this game?

(II) What is the probability that a participant successfully wins the first three levels in a row?

(Note: The die is a fair six-sided die with faces numbered 1 through 6. The number on the top face after each roll is the number obtained.)

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