
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
Every morning Absent-Minded Scientist goes to work, and in the evening, he returns home. The Scientist has two umbrellas and takes one with him only in one of two cases: either it is raining outside, or there is no umbrella where he is going. After a while, the Scientist calculated (and we remember that the Absent-Minded Scientist calculates everything) that he takes an umbrella with him in 20% of the cases. Find the probability of rain.

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