
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 sore knee. The doctor prescribed him 10 pills for his knee: taking one pill daily. These pills are effective in $90\%$ of cases, and in $2\%$ of cases, there is a side effect - absence of absent-mindedness, if it existed.

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 - knees stop hurting.

The bottles with pills look similar, and when the Scientist left for a ten-day business trip, he took one bottle with him, but paid no attention to which one. He took one pill a day for ten days and returned completely healthy. Both absent-mindedness and knee pain were gone. 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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