
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
To alleviate traffic pressure, a special railway line is constructed between two cities in a certain province, with a train serving as public transportation. It is known that the daily round trips ($y$) is a first-order function of the number of carriages dragged each time ($x$). If this train drags 4 carriages each time, it can make 16 round trips per day; if it drags 6 carriages each time, it can make 10 round trips per day. The number of carriages dragged by the train each time is consistent, and each carriage can carry 110 passengers when fully loaded.
(1) Find the function of $y$ with respect to $x$;
(2) When the train is fully loaded, how many carriages should be dragged each time to maximize the daily operating number of passengers? And what is the maximum daily operating number of passengers?

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