
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
Master Jin is planning to change his car recently and has set his eyes on two domestically produced cars with the same price.

| Type of Car | Fuel Car | New Energy Car |
| --- | --- | --- |
| Fuel Tank Capacity | $40$ liters | - |
| Fuel Price | $9$ yuan per liter | - |
| Battery Capacity | - | $60$ kilowatt-hours |
| Electricity Price | - | $0.6$ yuan per kilowatt-hour |
| Range | $a$ kilometers | $a$ kilometers |
| Cost per kilometer | $\frac{40 \times 9}{a}$ yuan | $\frac{36}{a}$ yuan |

$(1)$ Express the cost per kilometer of the new energy car in terms of $a$.  
$(2)$ If the cost per kilometer of the fuel car is $0.54$ yuan more than that of the new energy car.  
① Calculate the cost per kilometer of these two cars.  
② If the annual other expenses for the fuel car and the new energy car are $4800$ yuan and $7500$ yuan respectively. What is the annual mileage at which the annual cost of buying a new energy car is lower? (Annual cost $=$ Annual driving cost $+$ Annual other expenses)

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