
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. The original price for each room per day is 190 yuan. When the price is reduced to 180 yuan per room per day, the hotel will be fully booked. For every 10 yuan increase in the room price, one room will be vacant (the pricing department stipulates that the cost of staying in such hotels should not exceed 1.5 times the original price). If there are guests staying, the hotel needs to pay 20 yuan per room per day.

(1) If the price of each room on a given day increases by x yuan compared to the price when the rooms are fully booked, the hotel will have guests in ______ rooms (expressed in an algebraic expression containing x).

(2) At what price per room will the hotel make a profit of 9450 yuan for the day?

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