
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 pack of 10 tablets for his absent-mindedness. The Scientist keeps these tablets in a cabinet. Whenever the Scientist experiences an episode of absent-mindedness (which occurs several times a week at random moments), he opens the cabinet, takes out the pack, takes a tablet, and checks how many tablets he has left. If he sees that only one tablet is left, he immediately orders a new pack with instant delivery and puts it in the same cabinet on the same shelf.

If he sees the current pack is empty, he immediately throws it into the trash.

What is the probability that at 10:00 AM on December 31, the Absent-Minded Scientist has exactly two packs of tablets in the cabinet?

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