
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 tour group of 50 people stays at a hotel, which offers triple rooms, double rooms, and single rooms. The cost per person per night is 100 yuan for triple rooms, 150 yuan for double rooms, and 200 yuan for single rooms. If the group fills 20 rooms, calculate the minimum total cost.

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