
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

The cost of traveling on a toll road section depends on the vehicle class: passenger cars belong to the first class, for which the travel cost is 200 rubles, while light trucks and minibuses belong to the second class, for which the cost is 300 rubles.

At the toll payment point, an automatic system is installed which measures the height of the vehicle. If the height of the vehicle is below a certain threshold value \(h\), the system automatically categorizes it as class 1, and if it is above \(h\), it is categorized as class 2. However, errors are possible. For example, a low minibus might be categorized as class 1, which would make its driver happy. A passenger UAZ may be mistakenly categorized as class 2, and its driver would not be pleased. He may file a claim, and the operating company would have to refund him 100 rubles.

The company's management tasked the engineers to adjust the system so that the number of errors is minimized.

For several weeks, engineers collected data on vehicle heights passing through the toll point. They collected separate data for class 1 and class 2 vehicles. Along the x-axis, the vehicle height (in cm) is plotted, and along the y-axis, the average number of vehicles of that height passing through the toll point per day is shown. To visualize the data, points are connected by a smooth line.

Given this information and the graphs, the engineers are now pondering how to determine the threshold value \(h\) so that the probability of error is minimized. Solve this problem for them.

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