
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
There is a large bridge that is both a congested traffic area and a high accident-prone area. To ensure safety, the transportation department stipulates that the relationship between the distance $d(m)$ between cars on the bridge, the speed $v(km/h)$, and the length of the car $l(m)$ satisfies: $d=kv^{2}l+ \frac {1}{2}l(k$ is a positive constant). Assume that the length of all cars on the bridge is $4m$. When the speed is $60km/h$, the distance between cars is $2.66$ car lengths.

(1) Write the functional relationship of the car distance $d$ with respect to the car speed $v$;

(2) How should the speed be regulated to allow the maximum number of vehicles to pass through the bridge per hour?

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