
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 depends on the class of the vehicle: passenger cars belong to the first class, and for them, the travel cost is 200 rubles, while light trucks and minibusses belong to the second class, for which the cost is 300 rubles.

An automatic system at the toll booth measures the height of the vehicle. If the vehicle height is below a certain threshold value \(h\), the system classifies it as class 1, and if it is above \(h\), it is classified as class 2. Errors are possible. For example, a low minibus might be classified as class 1, making the driver happy. A passenger car like the UAZ may be mistakenly classified as class 2, and the driver can submit a claim, prompting the company to refund 100 rubles to the driver.

The company management has tasked engineers with adjusting the system so that the number of errors is minimized.

For several weeks, engineers collected data on the height of vehicles passing through the toll booth, separately for class 1 and class 2 vehicles. On the x-axis is the vehicle height (in cm), and on the y-axis is the average number of vehicles of that height passing through the toll booth each day. The points are connected by a smooth line for clarity.

Using this data and the graphs they constructed, the engineers need to determine the threshold value \(h\) that minimizes the probability of error.

Solve this problem for them.

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