
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
Currently, China's water environment issues have reached a critical point, and the $COD$ sensor for online monitoring of water quality in rivers is crucial for monitoring unorganized sources of pollution. The sensor conducts 24-hour online data collection and communication, with real-time alarm functions and statistical analysis reports, which greatly help in environmental protection. When the sensor moves against the flow in the water, the energy consumed is given by $E=kv^{2}t$, where $v$ is the speed of the sensor in still water (unit: $km$∕$h), $t$ is the time of travel (unit: $h)$, and $k$ is a constant. If the water flow speed in the river to be measured is $3km$∕$h, the energy consumed by the sensor traveling $10km$ against the flow is denoted as $E$. <br/>$(1)$ Find the function relationship of $E$ with respect to $v$; <br/>$(2)$ At what value of $v$ does the sensor consume the least energy $E$? Also, determine the minimum value of $E$.

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