
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 focus pills. The Scientist keeps the pills 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 pack, consumes a pill, and checks how many pills remain.

If the Scientist notices that only one pill is left, he immediately orders an identical new pack from the pharmacy with instant delivery and puts the new pack in the same cabinet.

If the Scientist sees that a pack is empty, he immediately throws it away.

What is the probability that at 10 o'clock in the morning on December 31st, the Absent-Minded Scientist will have exactly two packs of focus pills in his cabinet?

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