
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
After long-term observation, it is found that in busy traffic periods, the function relationship between the traffic flow $y$ (in thousand vehicles per hour) on a certain section of a highway and the average speed of cars $v$ (in kilometers per hour) is given by: $y=\frac{920v}{{v}^{2}+3v+1600}$ ($v \gt 0$). <br/>$(1)$ During this period, at what average speed $v$ will the traffic flow be maximized? What is the maximum traffic flow? (Keep the answer in fraction form) <br/>$(2)$ If the traffic flow needs to exceed $10$ thousand vehicles per hour during this period, in what range should the average speed of cars be?

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