
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
There are 6 rooms in the lodge and 7 friends checking in for the night. Determine the number of different ways the rooms can be assigned to the friends with no more than 2 friends per room, leaving at least one room unoccupied.

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