
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
It has been observed that the traffic flow $y$ (in thousands of vehicles per hour) on a certain section of highway during a certain time period has a functional relationship with the average speed $v$ (in kilometers per hour) of the vehicles: $y = \frac{920v}{v^2 + 3v + 1600} (v > 0)$.

(1) During this time period, what average speed $v$ results in the maximum traffic flow $y$? What is the maximum traffic flow? (Round to two decimal places)

(2) To ensure that the traffic flow during this time period is at least 10 thousand vehicles per hour, what range should the average speed of the vehicles be controlled within?

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