
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 statistical table shows that the fuel consumption rate $y$ (in liters) per hour of a certain car model during constant speed driving is related to the driving speed $x$ (in kilometers per hour) and can be represented by the function: $y = \frac{1}{128000}x^3 - \frac{3}{80}x + 8 (0 < x \leqslant 120).$ It is known that the distance between cities A and B is $100$ kilometers.

(1) How much fuel does the car consume when driving at a constant speed of $40$ kilometers per hour from city A to city B?

(2) At what constant speed should the car travel to consume the least amount of fuel from city A to city B? What is the minimum fuel consumption?

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