
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
In a "level passing game" rule, in the \( n \)-th level, a die needs to be rolled \( n \) times. If the sum of the points appearing in these \( n \) rolls exceeds \( 2^n \), then the level is considered passed. Questions:
(I) What is the maximum number of levels a person can pass in this game?
(II) What is the probability of passing the first three levels consecutively?
(Note: A die is a uniform cube with points \( 1, 2, 3, 4, 5, 6 \) on each face, and the number facing up after the die comes to rest is the point that appears.)

(2004 Annual High School Math Competition)

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