
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 the Absent-Minded Scientist a package with 10 tablets for absent-mindedness. The Scientist keeps the tablets in a cabinet. Whenever the Scientist experiences a bout of absent-mindedness (which happens several times a week at random times), he opens the cabinet, takes the package from the shelf, takes a tablet, and checks how many tablets are left. If the Scientist sees that only one tablet is left, he immediately orders an identical new package from the pharmacy with instant delivery and places it in the cabinet on the same shelf.

If the Scientist sees that the current package is empty, he immediately throws it into the trash can.

What is the probability that at 10 AM on December 31, the Absent-Minded Scientist will have exactly two packages of tablets for absent-mindedness in his cabinet?

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