
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 hotel has 50 rooms available for guests. When each room is priced at 180 yuan, all the rooms will be occupied; for every 10 yuan increase in the price per room, one room will be left vacant. If a guest stays in a room, the hotel will incur various expenses of 20 yuan per room per day. At what room price will the hotel's profit be maximized?

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