
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
Thirteen millionaires arrived at an economic forum and stayed at the "Super Luxury+" hotel. The hotel has rooms of 3 different types: 6-star, 7-star, and 8-star. We need to allocate the millionaires to these rooms in such a way that all three types of rooms are used (i.e., at least one person must stay in a 6-star room, at least one person in a 7-star room, and at least one person in an 8-star room). Additionally, a richer millionaire cannot stay in a room with fewer stars than a less wealthy one.

In how many ways can they be allocated given that the state of wealth for all millionaires is pairwise different?

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