
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
Two straight roads intersect perpendicularly. On one road, a car starts from a distance of $l_{1}=80 \mathrm{~km}$ from the intersection and heads towards the intersection at a constant speed of $v_{1}=80 \mathrm{~km/h}$. On the other road, another car starts at the same time from a distance of $l_{2}=60 \mathrm{~km}$ from the intersection, traveling towards the intersection at a speed of $v_{2}=60 \mathrm{~km/h}$. How fast is the distance between the cars changing? What is the situation if the initial distances are $l_{1}=l_{2}^{\prime}=80 \mathrm{~km}$? How much time after departure will the two cars be closest to each other, and what is this distance in both cases?

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