
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 four-star hotel has 300 rooms and charges 200 yuan per room per night with full occupancy every day. The hotel wants to upgrade to a five-star category and increase the room rate. It is found that for every 20 yuan increase in the room charge per day per room, the number of rooms occupied decreases by 10. If no other factors are considered, to what amount should the hotel raise its room rate to maximize its total daily income from the rooms?

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