
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

In a small town, there's only one bus company that transports people to a major district center. Additionally, there's a station for a dead-end railway line in the town, from which trains currently travel to the same center. The overall demand for bus and train transportation is determined by the function \( q(p) = 4200 - 100p \), where \( p \) is the minimum fare for a round trip on the bus or train, and \( q \) is the number of people wishing to travel at price \( p \).

It is known that train transportation is regulated by the government, so the fare for a round trip by train is fixed at 4 units. However, the train can transport no more than 800 people.

(a) What fare will the bus company set if its costs for transporting any number of passengers \( y \) are given by \( TC(y) = 10y + 225 \)?

(b) There are rumors in the town that due to the unprofitability of train transportation, the railway station will soon close. As a result, it will be possible to get to the center (and return) only by bus. How will the total number of transported passengers change in this case?

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