
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
A travel agency has 120 rooms, with a daily rental rate of 50 yuan per room, and they are fully booked every day. After renovation, the agency plans to increase the rental rate. Market research indicates that for every 5 yuan increase in the daily rental rate per room, the number of rooms rented out each day will decrease by 6. Without considering other factors, to what amount should the agency increase the daily rental rate per room to maximize the total daily rental income? And how much more will this be compared to the total daily rental income before the renovation?

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