
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
In recent years, urban traffic congestion has become severe, and major streets in a certain urban area often experience traffic jams. Electric bicycles, due to their small size, strong flexibility, and ease of operation, have become a common means of transportation for residents. According to observations, during peak travel hours, the flow of electric bicycles $Q$ (in thousands of vehicles per hour) on a certain section of road is related to the average speed of electric bicycles $v$ (in kilometers per hour) by the following function: $Q(v)=\frac{600v}{v^2+2v+400}$ (where $0<v\leq25$). <br/>$(1)$ To ensure that the flow of electric bicycles is not less than $10$ thousand vehicles per hour, find the range of values for $v$; <br/>$(2)$ When the flow of electric bicycles $Q$ is at its maximum, find the value of $v$ and estimate the maximum flow (rounded to $0.1$).

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