
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
China has become the world's largest electric vehicle market. Electric vehicles have significant advantages over traditional vehicles in ensuring energy security and improving air quality. After comparing a certain electric vehicle with a certain fuel vehicle, it was found that the average charging cost per kilometer for electric vehicles is $0.6$ yuan less than the average refueling cost per kilometer for fuel vehicles. If the charging cost and refueling cost are both $300$ yuan, the total distance that the electric vehicle can travel is 4 times that of the fuel vehicle. Let the average charging cost per kilometer for this electric vehicle be $x$ yuan.
$(1)$ When the charging cost is $300$ yuan, the total distance this electric vehicle can travel is ______ kilometers. (Express using an algebraic expression with $x$)
$(2)$ Please calculate the average travel cost per kilometer for these two vehicles separately.
$(3)$ If the other annual costs for the fuel vehicle and electric vehicle are $4800$ yuan and $7800$ yuan respectively, in what range of annual mileage is the annual cost of buying an electric vehicle lower? (Annual cost $=$ annual travel cost $+$ annual other costs)

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