
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 large district center. Additionally, the town has a terminal railway station from which currently trains go to the same center. The combined demand for bus and train rides is determined according to the function \( q(p) = 3000 - 20p \), where \( p \) is the minimum of the prices for a round trip by bus or train, and \( q \) is the number of people wanting to travel at price \( p \).

It is known that railway transportation is regulated by the state, so the round-trip fare on the train is fixed at 10 units. However, the train can carry no more than 1000 passengers.

(a) What price will the bus company set for the trip if its transportation costs for any number of passengers \( y \) are \( TC(y) = y + 5 \)?

(b) Rumors are circulating in the town that due to the unprofitability of railway transportation, the railway station will soon close, meaning the only way to get to the center (and back) 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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