
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
Given a hotel with 50 rooms, each priced at 180 yuan per day, and for every 10 yuan increase in the room price, one room is left vacant, determine the daily price per room that maximizes the hotel's profit, considering a fixed maintenance cost of 20 yuan per room per day.

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