
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
The Absent-Minded Scientist had a sore knee. The doctor prescribed him 10 pills for his knee: take one pill daily. The pills are effective in $90\%$ of cases, and in $2\%$ of cases, there is a side effect—absent-mindedness disappears, if present.

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

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

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