
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
The Yihuang Expressway connects the cities of Yichang, Wuhan, and Huangshi, with a total length of approximately 350 kilometers. It is one of the main arterial highways of the economic triangle in Hubei Province. If a vehicle enters the expressway and travels at a constant speed that is not less than 60 kilometers per hour and not more than 120 kilometers per hour, it is known that the vehicle's hourly transportation cost consists of a fixed part and a variable part. The fixed part is 200 yuan, and the variable part is proportional to the square of the speed \(v\) (in kilometers per hour), with a proportional constant denoted as \(k\). When the vehicle travels at the maximum speed, the hourly transportation cost is 488 yuan. To minimize the total transportation cost of the vehicle over the entire route, its speed should be \_\_\_\_\_\_.

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