
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
Given the relationship between the speed of a car $v$ and the cost of fuel per kilometer $w$ is given by the formula $w=\frac{1}{300} \cdot \frac{{v}^{2}}{(v-40)}$, where $60≤v≤120$, determine the value of $v$ when the cost of fuel per kilometer is at its minimum.

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