
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
The upcoming intercity railway lines between Shanghai and its surrounding cities will significantly alleviate traffic pressure and accelerate the flow between cities. According to calculations, if a train drags 4 carriages each time, it can make 16 round trips per day; if a train drags 7 carriages each time, it can make 10 round trips per day. The number of round trips per day, $t$, is a function of the number of carriages dragged each time, $n$.

1. Write the functional relationship between $n$ and $t$;
2. Each carriage can carry 110 passengers each time. How many carriages should be dragged each time to maximize the number of passengers per day, $y$? Also, find the maximum number of passengers per day. (Note: The number of passengers refers to the number of people transported by the train.)

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