
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
The village council of the secret pipeline is gathering around a round table, where each arriving member can sit in any available seat. How many different seating arrangements are possible if 7 participants join the council? (Two arrangements are considered identical if the same people are sitting to the left and right of each participant, and empty seats are not considered.)

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