
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 "passing game" follows these rules: At the nth level, a die is thrown n times. If the sum of the points from these n throws is greater than \(2^n\), the player passes the level. Questions:
(1) What is the maximum number of levels a player can pass in this game?
(2) What is the probability of passing the first three levels consecutively?
(Note: The die is a fair cube with faces showing 1, 2, 3, 4, 5, 6 points. After a throw, the number shown on the top face when the die comes to rest is the point rolled.)

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