
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 "clearance game" has the following rules: in the $n$-th round, a die is rolled $n$ times. If the sum of the points from these $n$ rolls is greater than $2^n$, then the player clears the round. Questions:
(1) What is the maximum number of rounds a player can clear in this game?
(2) What is the probability of clearing the first three rounds consecutively?
(Note: The die is a uniform cube with the numbers $1, 2, 3, 4, 5, 6$ on its faces. After rolling, the number on the top face is the result of the roll.)

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