
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 is only one bus company that transports people to a major district center. Additionally, there is a station for a terminal railway line, which currently runs electric trains to the same center. The total demand for bus and train transportation is determined by the function $q(p) = 3000 - 20p$, where $p$ is the minimum fare for a round trip to the center by bus or train, and $q$ is the number of people willing to make the trip at price $p$.

It is known that train transportation is regulated by the state, so the fare for a round trip by train is fixed at 10 units. However, the train can transport no more than 1000 people.

(a) What price will the bus company set for the fare if its transportation cost for any number of passengers $y$ is $TC(y) = y + 5$?

(b) There are rumors in the town that due to the unprofitability of train transportation, the train station will soon close, making the bus the only means to get to the center and back. 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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