
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
On a busy one-way motorway, vehicles operate under the following rule: the distance from the rear of one vehicle to the front of the following vehicle is one car length for each 10 kilometers per hour of speed (rounding up if not a multiple of 10). A sensor beside the road counts the number of vehicles that pass in an hour. Given that each vehicle is 5 meters long and vehicles vary in speed with speeds in multiples of 10 km/h up to a maximum of 100 km/h, find $N$, the maximum number of vehicles that pass the sensor in one hour and determine $N \mod 15$.

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