
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
A small hydropower station has a generator output power of $24.5\,kW$ and an output voltage of $350\,V$. The total resistance of the transmission line is $4\,\Omega$. In order to make the power loss of the transmission line $5\%$ of the generator's output power, a step-up transformer needs to be installed at the generator, and a step-down transformer needs to be installed at the user end, as the required voltage for the user is $220\,V$. Calculate:

$(1)$ The current in the transmission line;

$(2)$ The turns ratio of the primary to secondary coils of the step-up transformer;

$(3)$ The turns ratio of the primary to secondary coils of the step-down transformer.

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