
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 to stay in. When each room is priced at $180$ yuan, all rooms will be occupied. However, when the price of each room increases by $10$ yuan, one room will be left unoccupied. The hotel spends $20$ yuan in various expenses for each room per day when guests occupy the rooms. What price per room maximizes the hotel's profit?

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