
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
In January, a doctor gave a Forgetful Scientist a package containing 10 pills for forgetfulness. The scientist keeps the pills in a cabinet. Whenever the scientist is overtaken by a bout of forgetfulness (which happens several times a week at random times), he opens the cabinet, takes the package from the shelf, takes a pill, and notes how many pills of forgetfulness he has left.

If the scientist sees that only one pill is left, he immediately orders an identical new package from the pharmacy with instant delivery and places it on the same shelf in the cabinet. If the scientist sees that a package is empty, he immediately throws it in the trash.

What is the probability that at 10:00 AM on December 31, the Forgetful Scientist will have exactly two packages of forgetfulness pills in his cabinet?

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