
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
Through observation, it has been found that there is a functional relationship between the traffic flow rate $y$ (thousands of vehicles per hour) and the average speed of vehicles $v$ (km/hour) on a certain section of highway during a certain time period:
$$y= \frac{920v}{v^2+3v+1600} \quad (v>0)$$
(1) During this time period, at which average speed $v$ is the traffic flow rate $y$ maximized? What is the maximum traffic flow rate? (Round to two decimal places.)
(2) To ensure that the traffic flow rate is at least 10 thousand vehicles per hour during this time period, what should be the range for the average speed of vehicles?

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