
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 opening of the Xiaoxikou Tunnel not only alleviated the traffic pressure between Sangzhi and Zhangjiajie but also shortened the travel time. However, for traffic safety, the transportation department has made the following regulations for vehicles traveling in the tunnel:
1. The maximum speed should not exceed 60 kilometers per hour;
2. The distance $d$ between vehicles is directly proportional to the product of the square of the speed $v$ (in kilometers per hour) and the length of the vehicle $s$ (in meters), with a proportionality constant $k$ ($k > 0$);
3. According to requirement 2, if the distance is less than half the length of the vehicle, then the distance is set to $\frac{s}{2}$. Assuming the length of the vehicle is approximately $s$ meters, when the speed is 50km/h, the distance is exactly the length of the vehicle.

(1) Please write the function relationship of $d$ with respect to $v$ (where $s$ is a constant);

(2) At what speed should the vehicle travel to maximize the traffic flow $Q = \frac{1000v}{d+s}$?

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