
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 length of a river. 
The Geographic Society of Anchuria (GSA) sent an expedition to measure the length of the great Anchurian river, Rio-Coralio. It turned out that the length from the source to the mouth is 402 km plus-minus 500 meters, with a probability of error of 0.04, and the errors in both positive and negative directions are equally probable.

Independently, the agency AWRA (Anchurian Water Resources) conducted its study on this topic. The result: 403 km plus-minus 500 meters. The probability of error is also 0.04, and again, errors in both positive and negative directions are equally probable.

When the results were compared and it was confirmed that there were no errors in methods and measurements, the president of GSA and the director of AWRA jointly approached the Scatterbrained Scientist, who is a recognized expert in statistics, to explain the discrepancy. The scientist was delighted and said: "Now I can accurately determine the length of Rio-Coralio with a small probability of error." How might he have reasoned? Find the estimate and the probability of error.


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