
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 ache. The doctor prescribed him 10 pills for the knee: take one pill daily. The pills work in 90% of cases, but in 2% of cases they have a side effect – the absent-mindedness disappears, if any.

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 knees stop hurting.

The jars with pills are similar, and when the Scientist went on a ten-day business trip, he took one jar with him but did not pay any attention to which one. For ten days he took one pill a day and returned completely healthy. Both the absent-mindedness was gone, and the knee didn’t hurt anymore. 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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