
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 player throws a fair die (with each number from 1 to 6 having an equal probability of 1/6 and each throw being independent) repeatedly until their total score is greater than or equal to \( n \). Let \( p(n) \) be the probability that their final score is exactly \( n \). Find \( \lim_{n \to \infty} p(n) \).

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