
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 gives Absent-Minded Scientist a pack containing 10 tablets for his 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 a tablet from the pack, and checks how many tablets he has left. If the scientist sees that there is only one tablet left, he immediately orders an identical new pack from the pharmacy with instant delivery and places it in the same cabinet on the same shelf.

If the scientist sees that the current pack is empty, he immediately throws it in the trash bin.

What is the probability that at 10 a.m. on December 31st, the Absent-Minded Scientist will have exactly two packs of tablets in his cabinet?

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