
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

Absent-Minded Scientist had a knee pain. The doctor prescribed him 10 pills for the knees: take one pill daily. The pills are effective $90\%$ of the time, and in $2\%$ of the cases, a side effect occurs – the absent-mindedness disappears if it was present.

Another doctor prescribed the Scientist pills for absent-mindedness – also one per day for 10 days. These pills cure absent-mindedness $80\%$ of the time, but in $5\%$ of the cases, there is a side effect – the knee pain stops.

The pill bottles look similar, and when the Scientist went on a ten-day business trip, he took one bottle with him but did not pay attention to which one it was. For ten days, he took one pill a day and returned completely healthy. Both his absent-mindedness and knee pain were cured. Find the probability that the Scientist took the pills for absent-mindedness.

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