
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

A small town has only one bus company that transports people to a major district center. Additionally, the town has a station of a dead-end railway line, from which trains currently run to the same center. The combined demand for bus and train travel is determined by the function $q(p) = 4200 - 100p$, where $p$ is the minimum fare for a round trip by bus or train, and $q$ is the number of people willing to travel at price $p$.

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

(a) What fare will the bus company set if its cost of transporting any number of passengers $y$ is given by $T C(y) = 10y + 225$?

(b) There are rumors in the town that the railway station might soon close due to the unprofitability of train transportation, meaning that the only way to get to and from the center will be by bus. How will the total number of passengers transported change in this case?

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