
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
In recent years, with the popularization of the concept of "low-carbon living, green travel," new energy vehicles have become the mainstream trend in the automotive industry in China. A certain car manufacturer has developed a new type of electric vehicle and plans to produce and install 288 vehicles in a year. They have reassigned some skilled workers and recruited new workers to complete the installation of the new electric vehicles after training. After a period of time, the research department found that 2 skilled workers and 1 new worker can install 10 electric vehicles per month, and 1 skilled worker and 3 new workers can also install 10 electric vehicles per month. 

$(1)$ Find the number of electric vehicles that each skilled worker and each new worker can install per month. 

$(2)$ In a comparative survey between this electric vehicle and a certain gasoline vehicle, it was found that the average cost per kilometer of the electric vehicle is $0.6$ yuan less than that of the gasoline vehicle. When the cost per kilometer of both vehicles is $200$ yuan, the electric vehicle can travel four times the total distance of the gasoline vehicle. 

① Find the average cost per kilometer of this electric vehicle. 

② If the annual other expenses for the electric vehicle and the gasoline vehicle are $6400$ yuan and $4000$ yuan respectively. When the annual mileage is how many kilometers, is the annual cost of buying an electric vehicle lower? (Annual cost = annual travel cost + annual other expenses)

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