
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 100 identical rooms, the occupancy rate and price per room per day are related as shown below:

| Price per room per day | $200$ yuan | $180$ yuan | $160$ yuan | $140$ yuan |
|------------------------|------------|------------|------------|------------|
| Occupancy rate         | $65\%$     | $75\%$     | $85\%$     | $95\%$     |

Determine the price per room per day that maximizes the daily income.

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