
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 cars, initially 120 km apart, are moving in the same direction on a highway where the speed limit is 60 km/h. At a certain point on the highway, the speed limit increases to 70 km/h. Every 100 km from this point, the speed limit increases by 10 km/h (i.e., 100 km after the first point it goes up to 80 km/h, another 100 km further it becomes 90 km/h, and so on), until it reaches 120 km/h. At any given moment, the cars drive at the maximum allowed speed. What will be the distance (in km) between the cars when both are traveling at 120 km/h? If necessary, round the answer to two decimal places.

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