
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
According to statistics, a certain type of car has a maximum speed of $120$ kilometers per hour. When driving at a constant speed, the fuel consumption per hour $y$ (liters) is related to the driving speed $x$ (kilometers per hour) by the following function: $y=\frac{1}{128000}x^{3}-\frac{3}{80}x+8$. It is known that the distance between two places, A and B, is $100$ kilometers.

$(1)$ If the car drives at a constant speed of $40$ kilometers per hour, how many liters of fuel are needed to travel from A to B?

$(2)$ At what speed should the car drive at a constant speed to minimize the fuel consumption from A to B? What is the minimum amount of fuel needed?

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