
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 "pass level game" has the following rules: On the \( n \)-th level, a die is thrown \( n \) times. If the sum of the points that appear in these \( n \) throws is greater than \( 2^{n} \), then the player passes the level. 

1. What is the maximum number of levels a person can pass in this game?
2. What is the probability of passing the first three levels in a row?

(Note: The die is a fair six-faced cube with numbers \( 1, 2, 3, 4, 5, \) and \( 6 \). After the die is thrown and comes to rest, the number on the top face is the outcome.)

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