
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
There are two significant cities with frequent personnel exchanges. To alleviate traffic pressure, a dedicated railway line has been built, using a train for transportation. It is known that this train can pull 4 carriages and can make 16 round trips per day. If it pulls 7 carriages instead, it can make 10 round trips per day.  
(1) Assuming that the daily number of round trips is a linear function of the number of carriages pulled each trip, find the equation of this linear function.  
(2) Under the condition of (1), each carriage can carry 110 passengers. How many round trips must the train make per day to maximize the number of people transported? Also, find the maximum number of people transported per day.

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