
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
Lil Wayne, the rain god, determines the weather. If Lil Wayne makes it rain on any given day, the probability that he makes it rain the next day is  $75\%$ . If Lil Wayne doesn't make it rain on one day, the probability that he makes it rain the next day is  $25\%$ . He decides not to make it rain today. Find the smallest positive integer  $n$  such that the probability that Lil Wayne *makes it rain*  $n$  days from today is greater than  $49.9\%$ .

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