
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
At Ikervár (Vas County), the fall of the Rába River is used to drive dynamo machines. The produced electrical energy is also transmitted to the city of Sopron, which is $68 \mathrm{~km}$ away. Suppose $300 ~\mathrm{hp}$ needs to be sent to Sopron, but no more than $10 \%$ of this energy should be lost in the long transmission line. The voltage of the current starting from Ikervár is $20000 ~\mathrm{V}$. What diameter (in mm) of copper wire must be used to meet these conditions? The resistance of a $1 \mathrm{~m}$ long copper wire with a cross-sectional area of $1 \mathrm{~mm}^{2}$ is $\frac{1}{55} ~\mathrm{ohm}$.

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