
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," the rules stipulate: On the \( n \)th level, a player must roll a fair six-sided die \( n \) times. If the sum of the results from these \( n \) rolls exceeds \( 2^n \), the player passes the level. 

1. What is the maximum number of levels a player can pass in this game?
2. What is the probability that a player passes the first three levels consecutively?

Note: The die is a homogeneous cube with faces numbered \( 1, 2, 3, 4, 5, 6 \).

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