
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

On the bank of a river 100 meters wide, there is an electric plant situated. On the opposite bank, and 500 meters upstream, a factory is being constructed. Given that the river is straight between the plant and the factory, the cost of laying cables along the bank is 9 € per meter, and the cost of laying cables underwater is 15 € per meter, what is the length of the most economical cable route between the electric plant and the factory?

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